SSC CPO 2022 PYQ — Question 126

The correct answer is Option 1 i.e. $\frac{37}{16}$.

We know that,

sin 45° = $1\over \sqrt2$, cos 60° = $1\over2$, tan 45° = 1, cot 45° = 1

On putting the values in the given question

(sin⁴ 45°+ cos⁴ 60°) + (tan⁴ 45°+ cot⁴ 45°)

Putting the values of the angles in the above equation we get,

⇒ $({{1}\over {\sqrt2}})^4 + ({1\over 2})^4 + (1 + 1)$

⇒ ${1\over4} + {1\over16} + 2$ = $\frac{37}{16}$

Therefore, the value of (sin⁴ 45°+ cos⁴ 60°) + (tan⁴ 45°+ cot⁴ 45°) is $\frac{37}{16}$.