Question

This one is also trigonometry please answer with a pic

Answer 1

Answer:

$\huge{\blue{\bold{\underline{\mathbb{ÀnsWeR:-}}}}} \\ \\ (1 - {sin}^{2} \theta) \times {sec}^{2} \theta \: =1 \: \\ \rightarrow \: {cos}^{2} \theta \times {sec}^{2} \theta = 1 \: \: \: \: \: ( {sin}^{2} \theta \: + \: {cos}^{2} \theta = 1) \\ \rightarrow \: {cos}^{2} \theta \times \frac{1}{ {cos}^{2} \theta } = 1 \\ \rightarrow \: 1 = 1 \\ l.h.s = r.h.s$

$\huge{\bold{ \mathcal{ \blue{hence \: proved}}}}$

Hope it helps you....✌✌

Answer 2

Question :-

Prove that

$(1 - \sin {}^{2} (x) ) \times \sec {}^{2} (x) = 1$

Solution :-

Take LHS

$(1 - \sin {}^{2} (x) ) \times \sec {}^{2} ( x)$

As,

$1 - \sin {}^{2} (x) = \cos {}^{2} (x) \\ \\ and \: \: \: \: \: \: \sec {}^{2} (x) = \frac{1}{ \cos {}^{2} (x) }$

Hence,

$\cos {}^{2} (x) \times \frac{1}{ \cos {}^{2} (x) } = 1 \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: 1 = 1$

LHS =RHS - - - (PROVED)