Question

Trignometry question ::

If 7sin²A + 3cos²A = 4, show that tanA = 1/root3​

Answer 1

$\fbox{\texttt{\green{Given:}}}$

$\bold{7sin^2A+3cos^2A=4}$

$\fbox{\texttt{\orange{To\:prove:}}}$

$\bold{tanA=\frac{1}{\sqrt{3}}}$

$\fbox{\texttt{\blue{Identity\:used:}}}$

$\bold{sin^2\theta+cos^2\theta=1}$

$\fbox{\texttt{\red{How\:to\:Prove:}}}$

Given, $\bold{7sin^2A+3cos^2A=4}$

$\implies\bold{7sin^2A+3(1-sin^2A)=4}$

$\implies\bold{7sin^2A+3-3sin^2A=4}$

$\implies\bold{4sin^2A=1}$

$\implies\bold{sin^2A=\frac{1}{4}}$

$\implies\bold{sinA=\sqrt{\frac{1}{4}}=\frac{1}{2}}$

$\implies\bold{sinA=sin30^{\circ}}$

$\implies\bold{A=30^{\circ}}$

$\therefore\bold{tanA=tan30^{\circ}=\frac{1}{\sqrt{3}}}$

$\hrulefill$

★ Some other trigonometric identities :

• $\bold{1+tan^2\theta=sec^2\theta}$

• $\bold{1+cot^2\theta=cosec^2\theta}$