If sin α= P and tan α= Q, find the value of 1P2−1Q2 ?

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Question

If sin $α$ = P and tan $α$ = Q, find the value of $\frac{1}{P^{2}} - \frac{1}{Q^{2}}$ ?

Options:

A . 0

B . 1

C . 2

D . -1

Answer: Option B
:
B

Option (b)

Assume a 45-45-90 triangle

sin $α$ = P = $\frac{1}{\sqrt{2}}$ . (Sin= opposite side/ hypotenuse)

tan $α$ = Q = 1 (Tan = opposite side/ adjacent side)

$\frac{1}{P^{2}} - \frac{1}{Q^{2}}$ = 2-1 =1

Shortcut

$c o s e c^{2} α$ – $c o t^{2} α$ = 1 is a trigonometric identity

If you are not aware of this identity, substitute $α$ = 45.

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