jee-main 2025 Q20

jee-main · India · session1_29jan_shift2 Trig Proofs Power-Sum Evaluation via Trigonometric Constraint
If $\sin x + \sin ^ { 2 } x = 1 , x \in \left( 0 , \frac { \pi } { 2 } \right)$, then $\left( \cos ^ { 12 } x + \tan ^ { 12 } x \right) + 3 \left( \cos ^ { 10 } x + \tan ^ { 10 } x + \cos ^ { 8 } x + \tan ^ { 8 } x \right) + \left( \cos ^ { 6 } x + \tan ^ { 6 } x \right)$ is equal to :
(1) 4
(2) 1
(3) 3
(4) 2
If $\sin x + \sin ^ { 2 } x = 1 , x \in \left( 0 , \frac { \pi } { 2 } \right)$, then $\left( \cos ^ { 12 } x + \tan ^ { 12 } x \right) + 3 \left( \cos ^ { 10 } x + \tan ^ { 10 } x + \cos ^ { 8 } x + \tan ^ { 8 } x \right) + \left( \cos ^ { 6 } x + \tan ^ { 6 } x \right)$ is equal to :\\
(1) 4\\
(2) 1\\
(3) 3\\
(4) 2