Cos tan inverse x sin cot inverse 3 4
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Solve cos(tan inverse x) = sin(cot inverse 3/4)
Answered by admin @
Cos(tan⁻¹x)=sin(cot⁻¹3/4)
Let, cot⁻¹(3/4)=y
or, coty=3/4(=perpendicular/base)
Using Pythagorus's theorem,
hypotenuse=√(p²+b²)=√(3²+4²)=√25=5
∴, siny(=p/h)=3/5
∴, sin(cot⁻¹3/4)=siny=3/5
cos(tan⁻¹x)=3/5
or, tan⁻¹x=cos⁻¹(3/5)
Again let, cos⁻¹(3/5)=z
or, cosz=3/5=base/hypotenuse
∴, perpendicular=√5²-3²=√16=4
∴, tanz=p/b=4/3
∴, tan⁻¹x=z
or, x=tanz
or, x=4/3
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