If sin- P and tan- Q- find the value of 1- P 2-1- Q 2 -A- 0B- 1C- 2D- -1

The correct option is B 1Option (b) Assume a 45 45 90 triangle sin α= P = 1/√(2) . (Sin= opposite side/ hypotenuse) tan α= Q = 1 (Tan = opposite side/ adjace ...

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If sinα= P an...

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

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Solution

The correct option is A 1
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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If sin α= P and tan α= Q, find the value of 1P2−1Q2 ?

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