Question

1+sin theta/cos theta

Answer 1

The reciprocal cosine function is secant: sec(theta)=1/cos(theta). The reciprocal sine function is cosecant, csc(theta)=1/sin(theta).

And the 3 new functions are secant theta, cosecant theta and cotangent theta.

Answer 2

frac{\cos \theta }{1 + \sin \theta }= \frac{1 – \sin \theta }{cos\theta }[/latex]

Now will start with LHS

We will multiplu and divide Numeratir and denominator by 1-sinΘ

[latex]\frac{\cos \theta }{1 + \sin \theta }. \frac{1 -\sin \theta}{1 -\sin \theta}[/latex] [latex]\frac{\cos \theta .(1 -\sin \theta)}{1 -\sin^{2} \theta}[/latex]

Now we will use the identity

sin2x = 1-cos2x

[latex]\frac{\cos \theta .(1 -\sin \theta)}{\cos ^{2} \theta}[/latex] [latex]\frac{(1 -\sin \theta)}{\cos\theta}[/latex]

= RHS