Question

If 8 tan theta =15 find cos theta

Answer 1

it can be positive or negative depending on quadrant

Answer 2

Answer:

The value of  $cos\theta =\pm\dfrac{8}{17}$

Step-by-step explanation:

Given the value of $8 tan \theta =15$

Rewriting the equation,

$tan \theta =\dfrac{15}{8}$

Using $tan\theta =sin\theta/cos\theta$

$\implies \dfrac{sin\theta}{cos\theta}=\dfrac{15}{8}$

Using the trigonometric relation, $sin^2\theta+cos^2\theta=1$, $sin\theta$ can be written as

$\implies \dfrac{\sqrt{1-cos^2\theta} }{cos\theta}=\dfrac{15}{8}$

squaring on both sides,

$\dfrac{1-cos^2\theta }{cos^2\theta}=\dfrac{225}{64}$

$\implies (1-cos^2\theta )64=225\times cos^2\theta}$

$\implies 64-64cos^2\theta =225 cos^2\theta$

$\implies 225 cos^2\theta+64cos^2\theta -64=0$

$\implies 289cos^2\theta -64=0$

$\implies cos^2\theta =\dfrac{64}{289}$

$\implies cos\theta =\sqrt{\dfrac{64}{289}} =\pm\dfrac{8}{17}$

Therefore, the value of

$cos\theta =\pm\dfrac{8}{17}$

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