Question

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

Answer 1

Answer:

Step-by-step explanation:

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Answer 2

Answer:

$Value \:of \\sec\theta+cosec\theta=\frac{2\sqrt{3}+6}{3}$

Step-by-step explanation:

$Given\: 7sin^{2}\theta+3cos^{2}\theta=4$

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

/* By Trigonometric identity:

cos²A = 1-sin²A */

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

$\implies 4sin^{2}\theta=4-3$

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

$\implies sin\theta = \sqrt{\frac{1}{4}}\\=\frac{1}{2}\\=sin30\degree$

$\implies \theta = 30\degree$

$Now,\\sec\theta+cosec\theta\\=sec30\degree +cosec30\degree\\=\frac{2}{\sqrt{3}}+2\\=\frac{2\sqrt{3}}{3}+2\\=\frac{2\sqrt{3}+6}{3}$

Therefore,

$Value \:of \\sec\theta+cosec\theta=\frac{2\sqrt{3}+6}{3}$

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