Question

Without using trigonometric tables, evaluate 

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

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