If $p \sec 50^\circ = \tan 50^\circ$, then the value of p is : (a) $\tan 50^\circ$ (b) $\cos 50^\circ$ (c) $\sec 50^\circ$ (d) $\sin 50^\circ$

If p sec 50^° = tan 50^°, then the value of p is : (a) tan 50^° (b) cos 50^° (c) sec 50^° (d) sin 50^°

Question 26 of 36

p \sec 50^\circ = \tan 50^\circ

(a)

\tan 50^\circ

(b)

\cos 50^\circ

(c)

\sec 50^\circ

(d)

\sin 50^\circ

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Solving $p\sec50^\circ = \tan50^\circ$ gives $p = \sin50^\circ$ , so the answer is option (d).

We are given

$p\sec 50^\circ = \tan 50^\circ \;\Rightarrow\; p = \frac{\tan 50^\circ}{\sec 50^\circ}.$

Write each ratio in terms of sine and cosine:

$\tan 50^\circ = \frac{\sin 50^\circ}{\cos 50^\circ},\qquad \sec 50^\circ = \frac{1}{\cos 50^\circ}.$

Therefore

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