Question

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

Answer 1

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

Answer 2

Answer: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