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Prove these identities:

(i) Sin (x)/Sec (x) = 1/ Tan (x) + Cos (x)

(ii) 1 - Cos (x)/ Sin (x) = Sin (x) / 1 + Cos (x)

Question

(A reward will be given to the user with the best response)
Prove these identities:

(i) Sin (x)/Sec (x) = 1/ Tan (x) + Cos (x)

(ii) 1 - Cos (x)/ Sin (x) = Sin (x) / 1 + Cos (x)

anonymous · Answer

I solved the 2nd one for you if you take them as fractions like this

$$\frac{ 1-cosx }{ sinx }=\frac{ sinx }{ 1+cosx }$$

Cross multiply and you get

$$\sin^2x=1-\cos^2x$$

You will see something interesting if you add the cos part

$$\sin^2x + \cos^2x = 1$$

This is one of the Pythagorean identities meaning both sides are identical to one another