Question

sin7°^2+sec^223°+sin^283°_cot^267°

Answer 1

Answer:

2 + 2 tan^2 23 or 2 sec^2 23.

Step-by-step explanation:

Sin^2( 7) + sec^2 (23) + sin^2(83) + cot^2(67)

= sin^7 + sec^2 23 + cos^2 7 + tan^2 23

= 1 + 1 + tan^2 23 + tan^2 23

= 2 + 2 tan^2 23

Or

= 2 sec^2 23

Identity used :

Sin^2 A + cos^2 A = 1

Sec^2 A = 1 + tan^2 A

And

Cos A = sin (90 - A)

Cot A = tan (90 - A)

✅ 83 + 7 = 90 degree (complementary angles)

✅ 23 + 67 = 90 degree (complementary angles)