Question

without using trigonometric table prove that​

Answer 1

Answer

(i) LHS cos81° - sin9°

= cos(90° -9°)- sin9°

= sin9° sin9°

= 0

= RHS

(ii) LHS = tan71° - cot19°

=tan(90° 19°) - cot19°

=cot19° cot19° =0

= RHS

(iii) LHS = cosec80° - sec10°

= cosec (90° -10°) - sec(10°)

= sec10° sec10⁰

= 0

= RHS

(iv) cosec^2 72° - tan^2 18° = 1 LHS = cosec^2 72° - tan^2 18° = cosec^2 72° - tan2 (90-72) = cosec^2 72° - cot^2 72° = 1

(v) cos^2 75° + cos^2 15°

= 1 LHS = cos^2 75° + cos^2 15°

= cos^2 75° + cos^2 (90-75)°

= cos^2 75° + sin^2 75°

= RHS

(vi) tan^2 66° cot^2 24°

= 0 LHS tan^2 66° - cot^2 24°

= tan^2 66°-cot^2 (90-66)°

= tan^2 66° - tan^2 66° = 0

= RHS

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(viii) Eighth for your own effort.

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Answer 2

Step-by-step explanation:

(i) LHS cos81° - sin9°

= cos(90° -9°)- sin9°

= sin9° sin9°

= 0

= RHS

(ii) LHS = tan71° - cot19°

=tan(90° 19°) - cot19°

=cot19° cot19° =0

= RHS

(iii) LHS = cosec80° - sec10°

= cosec (90° -10°) - sec(10°)

= sec10° sec10⁰

= 0

= RHS

(iv) cosec^2 72° - tan^2 18° = 1 LHS = cosec^2 72° - tan^2 18° = cosec^2 72° - tan2 (90-72) = cosec^2 72° - cot^2 72° = 1

(v) cos^2 75° + cos^2 15°

= 1 LHS = cos^2 75° + cos^2 15°

= cos^2 75° + cos^2 (90-75)°

= cos^2 75° + sin^2 75°

= RHS

(vi) tan^2 66° cot^2 24°

= 0 LHS tan^2 66° - cot^2 24°

= tan^2 66°-cot^2 (90-66)°

= tan^2 66° - tan^2 66° = 0

=RHS.

with regards - Priyodipto Basak,

try to follow. m. e..