Cos tan 1 x sin cot 1 3 4

Asked by admin @ 13/08/2021 in Math viewed by 302 People

Solve the following equation for x:cos(tan-1 x )=sin(cot-1 3/4)

Answered by admin @ 13/08/2021

Basic Identities Used :-

$\boxed{ \sf \:cos( {cos}^{ - 1}x) = x \: if \: x \in \: [- 1,1]}$

$\boxed{ \sf \:sin({sin}^{ - 1}x) = x \: if \: x \in \: [- 1,1]}$

$\large\underline{\sf{Solution-}}$

Given that

$\rm :\longmapsto\:cos( {tan}^{ - 1}x) = sin\bigg( {cot}^{ - 1}\dfrac{3}{4} \bigg)$

$\rm :\longmapsto\:cos\bigg( {cos}^{ - 1}\dfrac{1}{ \sqrt{1 + {x}^{2} } } \bigg) = sin\bigg( {sin}^{ - 1}\dfrac{4}{5} \bigg)$

$\rm :\longmapsto\:\dfrac{1}{ \sqrt{1 + {x}^{2} } } = \dfrac{4}{5}$

On squaring both sides, we get

$\rm :\longmapsto\:\dfrac{1}{1 + {x}^{2} } = \dfrac{16}{25}$

$\rm :\longmapsto\:25 = 16 + 16 {x}^{2}$

$\rm :\longmapsto\:25 - 16 = 16 {x}^{2}$

$\rm :\longmapsto\:9 = 16 {x}^{2}$

$\rm :\longmapsto\: {x}^{2} = \dfrac{9}{16}$

$\bf\implies \:x = \: \pm \: \dfrac{3}{4}$

Additional Information :-

$\boxed{ \sf \: {sin}^{ - 1}x + {cos}^{ - 1}x = \dfrac{\pi}{2} \: \: if \: x \in \: [ - 1,1]}$

$\boxed{ \sf \: {tan}^{ - 1}x + {cot}^{ - 1}x = \dfrac{\pi}{2} \: \: if \: x \in \: ( - \infty , \infty )}$

$\boxed{ \sf \: {sec}^{ - 1}x + {cosec}^{ - 1}x = \dfrac{\pi}{2} \: \: if \: x \in \: ( - \infty , \infty )}$

$\boxed{ \sf \: {tan}^{ -1 }x + {tan}^{ - 1}y = {tan}^{ - 1}\bigg(\dfrac{x + y}{1 - xy}\bigg) \: \: if \: xy \leqslant 1}$

$\boxed{ \sf \: {tan}^{ -1 }x + {tan}^{ - 1}y =\pi + {tan}^{ - 1}\bigg(\dfrac{x + y}{1 - xy}\bigg) \:if \: xy > 1}$

$\boxed{ \sf \:2 {tan}^{ - 1}x = {tan}^{ - 1}\bigg(\dfrac{2x}{1-{x}^{2}}\bigg)}$

$\boxed{ \sf \:2 {tan}^{ - 1}x = {sin}^{ - 1}\bigg(\dfrac{2x}{1 + {x}^{2}}\bigg)}$

$\boxed{ \sf \:2 {tan}^{ - 1}x = {cos}^{ - 1}\bigg(\dfrac{1 - {x}^{2} }{1 + {x}^{2}}\bigg)}$

Similar Questions

Solve cos tan 1 x sin cot 1 3 4

Asked by admin @ 04/08/2021 in Math viewed by 393 persons

Solve the following equation for x:cos(tan-1 x )=sin(cot-1 3/4)

Cos tan inverse x sin cot inverse 3 4

Asked by admin @ 23/08/2021 in Math viewed by 431 persons

Solve cos(tan inverse x) = sin(cot inverse 3/4)

Cot^2x-tan^2x=1 for all values of x

Asked by maham237 @ 26/12/2020 in Mathematics viewed by 572 persons

Cot^2x-tan^2x=1 for all values of x true or false?

Sin 1 tan cos 1 cot sec cosec

Asked by admin @ 31/08/2021 in Math viewed by 350 persons

Sin(1+tan)+cos(1+cot)=sec+cosec

Cos sin 1 3 5 cot 1 3 2

Asked by admin @ 17/08/2021 in Math viewed by 297 persons

Provethat cos(sin-1 3/5 + cot-1 3/2) = 6/5 root 13

Sin theta 1 cos theta tan theta 1 cos theta

Asked by admin @ 02/08/2021 in Math viewed by 349 persons

Prove that sin theta/1-cos theta + tan theta/1+cos theta=sec theta *cosec theta + cot theta

Cos x sin x tan x sec x

Asked by admin @ 10/08/2021 in Math viewed by 392 persons

Prove that tan(x)sin(x) +cos(x) = sec(x)

Sin 2 sin 3 2 cos 3 cos tan

Asked by admin @ 20/08/2021 in Math viewed by 313 persons

Prove that : sin a - 2sin^3 a / 2cos^3 + cos a = tan a

1 cot a tan a sin a cos a

Asked by admin @ 23/08/2021 in Math viewed by 310 persons

Prove that ( 1 + cot A + tan A) ( sin A - cos A) = sec A/cosec2 -cosec/ sec2 A

Cos sin 1 cos sin 1 cosec cot

Asked by admin @ 10/08/2021 in Math viewed by 297 persons

Prove that cos -sin+1/cos+sin-1= cosec +cot

X = sin 1 2 θ , y = cos 1 2 θ , −π ≤ θ ≤ π

Asked by maham237 @ 27/12/2020 in Mathematics viewed by 335 persons

X = sin 1/2θ, y = cos 1/2θ, −π ≤ θ ≤ π(a) eliminate the parameter to find a cartesian equation of the curve.

X 1 x 3 then x 4 1 x 4

Asked by admin @ 03/08/2021 in Math viewed by 348 persons

If(x+1/x) =3 find the value of (x4+1/x4)

Solve 4 x 3 2 x 1 0

Asked by maham237 @ 20/02/2021 in Mathematics viewed by 392 persons

Solve 4(x - 3) - 2(x - 1) > 0.

1 sin 2 theta 3 sin theta cos theta

Asked by admin @ 20/08/2021 in Math viewed by 311 persons

If 1+sin^2 theta=3 sin theta cos theta then prove that tan theta=1 or 1/2

X 1 x 2 x 3 x 4 120

Asked by admin @ 12/08/2021 in Math viewed by 400 persons

(x-1)(x-2)(x-3)(x-4)=120

Most viewed questions in Math

What is the value of x in the expression

Asked by admin @ 13/08/2021 in Math viewed by 15155 persons

Shubham is facing south and moves 30 km

Asked by admin @ 10/08/2021 in Math viewed by 12987 persons

Prachi excellence in mathematics class 7 solutions pdf free download

Asked by admin @ 02/08/2021 in Math viewed by 12041 persons

Oxford new enjoying mathematics class 7 solutions chapter 1

Asked by admin @ 20/08/2021 in Math viewed by 11520 persons

Survey of various types of bank accounts icse project

Asked by admin @ 17/08/2021 in Math viewed by 11509 persons

The town of p is located at point x

Asked by admin @ 20/08/2021 in Math viewed by 11359 persons

A clock gains 4 minutes after every 4 minutes

Asked by admin @ 10/08/2021 in Math viewed by 10170 persons

Running a tuck shop or canteen maths project pdf

Asked by admin @ 13/08/2021 in Math viewed by 9384 persons

Paul is sixteenth from the front of the row

Asked by admin @ 17/08/2021 in Math viewed by 9352 persons

The average weight of 20 teachers is 80 kg

Asked by admin @ 11/08/2021 in Math viewed by 7524 persons

The number 567 xy is completely divisible by 30

Asked by admin @ 23/08/2021 in Math viewed by 7399 persons

In a row of friends tiya occupies fifteenth place

Asked by admin @ 16/08/2021 in Math viewed by 7208 persons

What would $ mean if fat is coded as

Asked by admin @ 13/08/2021 in Math viewed by 5275 persons

Consider a 3 digit integer x with distinct digits

Asked by admin @ 23/08/2021 in Math viewed by 4804 persons

Rahul went to his mother's mother in law

Asked by admin @ 29/08/2021 in Math viewed by 4179 persons