Question

(1+sinx)(1-sinx)=1/sec^2x

Answer 1

To solve the equation (1+sinx)(1-sinx)=1/sec²x, simplify both sides of the equation. Use the identity a² - b² = (a+b)(a-b) to simplify the equation. Finally, simplify the right side of the equation by rewriting 1/sec²x as cos²x.

Step-by-step explanation:

To solve the equation (1+sinx)(1-sinx)=1/sec²x, we need to simplify both sides of the equation separately.
Starting with the left side, we can use the identity a² - b² = (a+b)(a-b) to simplify the equation.

(1+sinx)(1-sinx) = 1² - sinx² = 1 - sin²x

Now, let's simplify the right side of the equation. Since secx is the reciprocal of cosx, we can write 1/sec²x as cos²x.

Putting it all together, the equation becomes:

1 - sin^2x = cos²x

Answer 2

`(1+\sin x)(1-\sin x)=(1)/(\sec^2x)\\\\L_s=1^2-\sin^2x=1-\sin^2x=\cos^2x\\\\Used:\ a^2-b^2=(a-b)(a+b)\ and\ \sin^2x+\cos^2x=1\to\cos^2x=1-\sin^2x\\\\R_s=(1)/(\left((1)/(\cos x)\right)^2)=(1)/((1)/(\cos^2x))=1\cdot(\cos^2x)/(1)=\cos^2x\\\\L_s=R_s`