Question

Cos2A÷1-sin2A=cosA+sinA÷cosA-sinA

Answer 1

Given,

Cos2A÷1-sin2A  ------------ I

To prove,

Cos2A÷1-sin2A=cosA+sinA÷cosA-sinA

We can use 2 formulas,

cos(2A) = $cos^{2}$A - $sin^{2}$A

and,

sin(2A) = 2 sin(A)cos(A)

We, also substitute 1 = $cos^{2}$A + $sin^{2}$A

NOW try to solve the question on you own, with the following substitutions.

Make sure you have tried before actually seeing the solution.

Now, our I, becomes,

[$cos^{2}$(A) - $sin^{2}$(A)] / [$sin^{2}$A + $cos^{2}$(A) - 2 sin(A)cos(A)]

Now, denominator can be brought to the square form, and numerator simplified as,

[cos(A) + sin(A)] * [cos(A) - sin(A)] / $[cos(A) - sin(A)]^{2}$

Now, we get

cosA+sinA / cosA-sinA

Hence ,

Cos2A÷1-sin2A=cosA+sinA÷cosA-sinA

Hence, proved.