Question

Prove that sin40° sec50° = 1

Answer 1

Given:

$\bold{\sin 40^{\circ} \sec 50^{\circ} =1}$

To prove:

1

Solution:

${\sin 40^{\circ} \sec 50^{\circ} =1$

Solve L.H.S part:

$\sin 40^{\circ} \frac{1}{\cos 50^{\circ}} =1\\\\\frac{\sin 40^{\circ}}{\cos 50^{\circ}}=1\\\\\frac{\sin 40^{\circ}}{\cos (90-40^{\circ})}=1\\\\\frac{\sin 40^{\circ}}{\sin 40^{\circ}}=1\\\\1=1$

L.H.S=R.H.S

Answer 2

L.H.S.

sin 40° sec 50°

=> sin (90°-50°) sec 50°

=> cos 50° × 1/cos 50°

=> 1 = R.H.S.

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