SSC CGL 2024 PYQ — Question 72

The correct answer is option 2 i.e. 17.

tanA + cotA = 2

⇒ tanA + 1/tanA = 2

⇒ tan²A + 1 = 2tanA   [Multiplying both sides by tanA]

⇒ tan²A - 2tanA + 1 = 0

⇒ (tanA - 1)² = 0

⇒ tanA = 1 = tan 45°

⇒ A = 45°

Now, 7tan⁸A - 6cot⁸A + 8sec²A = 7tan⁸45° - 6cot⁸45° + 8sec²45°

= 7(1)⁸ - 6(1)⁸ + 8(√2)²

= 7 - 6 + 16

= 17

Therefore, the required value is 17.