Question

sin^2theta /cos theta +cos theta =sec theta
​

Answer 1

AnswEr :

$\large\star\sf\frac{sin^2\theta}{cos\theta} + cos\theta \: = \: sec\theta$

$\bullet$ A basic tip for these type of questions is that we have to prove Left hand side(L.H.S) of question to the Right hand side (R.H.S) of question.

$\underline{\dag\:\textsf{Let's \: head \: to \: the \: question \: now:}}$

$\bullet$ Taking the left hand side of question

$\large\ : \implies\sf\frac{sin^2\theta}{cos\theta} + cos\theta$

$\scriptsize\sf{\: \: \: \: \: \:( \therefore\ \: \pink{Taking \: L.C.M}) }$

$\large\ : \implies\sf\frac{sin^2\theta + cos^2\theta}{cos\theta}$

$\scriptsize\sf{\: \: \: \: \: \:( \therefore\ \: \pink{ sin^2\theta + cos^2\theta = 1}) }$

$\large\ : \implies\sf\frac{1}{cos\theta}$

$\scriptsize\sf{\: \: \: \: \: \:( \therefore\ \: \pink{ sec\theta = \frac{1}{cos\theta} }) }$

$\normalsize\ : \implies\sf\ sec\theta$

$\bullet$ Here, we get the Right hand side of question.

$\normalsize\ : \implies\sf\ L.H.S = R.H.S$

$\large\ : \implies{\underline{\boxed{\sf{Hence \: proved!!}}}}$

Some important identities related to it :

$\boxed{\begin{minipage}{6cm} Important Trigonometric identities :- \\ \\ \: \: 1)\sin^2\theta+\cos^2\theta=1 \\ \\ 2)\sin^2\theta= 1-\cos^2\theta \\ \\ 3)\cos^2\theta=1-\sin^2\theta \\ \\ 4)1+\cot^2\theta=\text{cosec}^2 \, \theta \\ \\5) \text{cosec}^2 \, \theta-\cot^2\theta =1 \\ \\ 6)\text{cosec}^2 \, \theta= 1+\cot^2\theta \\\ \\ 7)\sec^2\theta=1+\tan^2\theta \\ \\ 8)\sec^2\theta-\tan^2\thetha=1 \\ \\ 9)\tan^2\theta=\sec^2\theta-1 \end{minipage}}$