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

If Sin α= P And Tan α= Q, Find The Value Of 1P2−1Q2 ?...

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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