Andhra Pradesh Board Solutions for Exercise 1: Exercise 6 (a)

Prove the following :

$3(\sin \theta -\cos \theta {)}^4+6(\sin \theta +\cos \theta {)}^2+4\left({\sin }^6\theta +{\cos }^6\theta \right)=13$

Prove that ${\cos }^4\alpha +2{\cos }^2\alpha \left(1-\frac{1}{{\sec }^2\alpha }\right)=\left(1-{\sin }^4\alpha \right)$.

Prove that $\frac{(1+\sin \theta -\cos \theta {)}^2}{(1+\sin \theta +\cos \theta {)}^2}=\frac{1-\cos \theta }{1+\cos \theta }$.

If $\frac{2\sin \theta }{(1+\cos \theta +\sin \theta )}=x$, then find the value of $\frac{(1-\cos \theta +\sin \theta )}{(1+\sin \theta )}$.

Eliminate $\theta$ from the following :

$x=a{\cos }^3\theta ;y=b{\sin }^3\theta$

Eliminate $\theta$ from the following :

$x=a{\cos }^4\theta ;y=b{\sin }^4\theta$

Eliminate $\theta$ from the following :

$x=a(\sec \theta +\tan \theta );y=b(\sec \theta -\tan \theta )$

Eliminate $\theta$ from the following :

$x=\cot \theta +\tan \theta ;y=\sec \theta -\cos \theta$