Question

Find the value of
(Cos × Sin^-1 √3/2)^2 + (tan × Cot^-1 1)^2​

Answer 1

Answer:

$\boxed{\red{\sf \left\{ cos \bigg( sin^{-1}\bigg(\dfrac{\sqrt3}{2}\bigg)\bigg)\right\}^2+\left\{ tan\bigg( cot^{-1}(1)\bigg)\right\}^2 =\dfrac{5}{4} }}$

Step-by-step explanation:

A trignometric expression is given to us and we need to find the value of that , expression . Some basic knowledge required here is , that , say if we have ,

$\sf\red{\dashrightarrow} tan\theta = x$

And we need to find the value of theta ,then the angle can be written as ,

$\sf\red{\dashrightarrow} \theta =tan^{-1}( x)$

Or else we know that , the value of tan 45° = 1 . We can write it as ,

$\sf\red{\dashrightarrow} \theta = 45 = tan^{-1}(1)$

.Now let's simplify out the equation . The given equation is ,

$\sf\red{\dashrightarrow} \left\{ cos \bigg( sin^{-1}\bigg(\dfrac{\sqrt3}{2}\bigg)\bigg)\right\}^2+\left\{ tan\bigg( cot^{-1}(1)\bigg)\right\}^2$

• We know that , the value of sin 60° = √3/2 and cot 45° = 1. So that ,

$\sf\red{\dashrightarrow} (cos 60^{\circ})^2 +( tan45^{\circ})^2 \\\\ \sf\red{\dashrightarrow} \bigg(\dfrac{1}{2}\bigg)^2 + 1^2 \\\\ \sf\red{\dashrightarrow} \dfrac{1}{4} + 1 \\\\ \sf\red{\dashrightarrow} \dfrac{ 4 + 1 }{4} \\\\ \sf\red{\dashrightarrow} \boxed{\pink{\sf \dfrac{5}{4}}}$

$\rule{200}2$