Question

Evaluate

sin^2 34° + sin^2 56° + 2tan18° tan72°​

Answer 1

`sin^2 34^@ + sin^2 56^@ + 2 tan 18^@ tan 72^@cot^2 30^@`:

= sin^2 34^2 + sin^2 (90^@ - 34^@) + 2 tan 18^@ tan (90^@ - 18^@)- cot^2 30^@

= sin^2 34^@ + cos^2 34^@ + 2tan 18^@ cot 18^@cot^2 30^@

= (sin^2 34^@ + cos^2 34^@) + 2 tan 18^@

xx 1/(tan 18^@) - cot^2 30^@

`= 1 + 2 xx 1- (sqrt3)^2`

= 1 + 2-3

= 3-3

= 0

Answer 2

Answer:

sin² 34° + sin ² 56° + 2tan 18° tan 72°

sin² 34° + sin² (90°-56°) + 2 tan 18° tan(90°-72°)

sin²34° + cos²34° + 2tan 18° cot 18°

(sin²34°+cos²24°) + 2 × tan 18° × 1/tan 18°

1+2×1

3