Question

prove that. sin²A+(1/1+tan²A)=1​

Answer 1

Answer:

$using \: \: \: \: 1 + \tan {}^{2} ( \alpha ) = \sec {}^{2} ( \alpha ) \\ \\ \sin {}^{2} (a) + \frac{1}{1 + \tan {}^{2} (a) } \\ sin {}^{2} (a) + \frac{1}{ \sec {}^{2} (a) } \\ sin {}^{2} (a) + \cos {}^{2} (a) \\ \\ now \: \sin ^{2} (x) + \cos {}^{2} (x) = 1 \\ \\ \\ \\ using \: it \\ sin {}^{2} a + \cos {}^{2} (a) = 1$

Answer 2

Answer:

sin²A+(1/1+tan²A)=1

Step-by-step explanation:

LHS-sin²A+(1/1+tan²A)

=>sin²A+1/sec²A

By formulae

[1+tan²A=sec²A,1/sec²A=cos²A]

=>sin²A+cos²A=1

Hence LHS=RHS

Proved.