Question

prove that 1 minus tan squared theta by 1 +tan square theta is equals to cos square theta minus sin square theta​

Answer 1

Given:

$\frac{1-tan^{2}x}{1+tan^{2}x}$

To Prove:

$\frac{1-tan^{2}x}{1+tan^{2}x} = cos^{2}x-sin^{2}x$

Proof:

To prove the given term take the LHS of the given term as solve accordingly to get the RHS of the given term

as we have given the trigonometric term that is tanx so change it into the sin and cos

so let's take the LHS of the given term

• $\frac{1-tan^{2}x}{1+tan^{2}x}$

• $\frac{1-\frac{sin^{2}x}{cos^{2}x}}{1+\frac{sin^{2}x}{cos^{2}x}}$

• $\frac{cos^{2}x-sin^{2}x}{cos^{2}x+sin^{2}x}$

From the identity of the trigonometry sin²x+cos²x = 1

so we get:

• $\frac{cos^{2}x-sin^{2}x}{1}$

• $cos^{2}x-sin^{2}x$

Hence LHS=RHS

Hence Proved

Answer 2

hope this was helpful.......