Question

Prove: sinx tanx + sinx/tanx = 1/cosx

Answer 1

Look at step-by-step explanation.

Explanation:

First write everything in terms of sin and cos:

(sinx)(sinx/cosx) + (sinx)/(sinx/cosx) = (1/cosx)

Then simplify the expression where you can:

(sin^2)/(cosx) + (cosx) = (1/cosx)

Next find a common denominator and add the two numbers on the left side of the equation:

(sin^2)/(cosx) + (cos^2x)/(cos^2x) = (1/cosx)

((sin2^x)+(cos2^x)/(cosx)) = (1/cos)

Finally, use the identity, sin2^x + cos2^x = 1, to simply to numerator:

(1/cosx) = (1/cosx)