Question

If 7 sin squared theta + 3 cos squared theta is equal to 4 then find the value of sec theta + cosec theta

Answer 1

seca=2/root3

coseca=2

Answer 2

Find the value:

Step-by-step explanation:

$\ Given \ value:\\\\7 \sin^2\theta+3\cos^2\theta =4\\\\\ find:\\\\ \sec\theta + \ cosec\ \theta = ?\\\\\ Solution:\\\\7 \sin^2\theta+3(1-\sin^2\theta) =4\\\\7 \sin^2\theta+3- 3\sin^2\theta =4\\\\4\sin^2\theta=4-3\\\\4\sin^2\theta=1\\\\\sin^2\theta = \frac{1}{4}\\\\\sin^2\theta = (\frac{1}{2})^2\\\\\sin\theta = (\frac{1}{2})\\\\\sin\theta = \sin\ 30\°\\\\\theta = 30\°$

$\rightarrow \sec\theta+\ cosec\theta= ?\\\\\rightarrow \sec\ 30\°+\ cosec\ 30\°= ?\\\\\rightarrow \frac {2}{\sqrt{3}}+ 2\\\\\rightarrow \frac {2}{\sqrt{3}}\times \frac{\sqrt{3}}{\sqrt{3}}+ 2\\\\\rightarrow \frac {2\sqrt{3}}{3}+ 2\\\\\rightarrow \frac {2\sqrt{3}+6}{3}\\\\\rightarrow \frac {2(\sqrt{3}+3)}{3}$

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