R S Aggarwal and Veena Aggarwal Solutions for Exercise 5: TEST YOURSELF

If $5 cot \theta =3$, show that the value of $\left(\frac{5 \sin \theta -3 \cos \theta }{4 \sin \theta +3 \cos \theta }\right)$ is $\frac{16}{29}$.

Prove that $\left(\sin {32}^{°} \cos {58}^{°}+\cos {32}^{°} \sin {58}^{°}\right)=1$.

If $x=a \sin \theta +b \cos \theta$ and $y=a \cos \theta - b \sin \theta$, prove that $x^2+y^2=a^2+b^2$.

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

Prove that $\frac{1}{\left(\sec \theta -\tan \theta \right)}-\frac{1}{\cos {\displaystyle }{\displaystyle \theta }}=\frac{1}{\cos {\displaystyle }{\displaystyle \theta }}-\frac{1}{\left(\sec \theta +\tan \theta \right)}$

Prove that $\frac{\left(\sin A- 2 {\sin }^3 A\right)}{\left(2 \cos A-\cos A\right)}=\tan A$.

Prove that  $\frac{\tan A}{\left(1-cot A\right)}+\frac{cot A}{\left(1-\tan A\right)}=\left(1+\tan A+cot A\right)$

If $\sec 5A=\mathrm{cosec} \left(A-{36}^{°}\right)$ and $5A$ is an acute angle, show that $A={21}^{°}$