Math, asked by jayantwaghmare, 1 year ago

if sin theta is equals to 7 upon 25 find the values of cos theta and tan theta

Answers

Answered by BrainlyVirat
5
Here's the answer

Given =>

 \sf{sin \: \theta = \frac{7}{25}}

We know that ,

 \sf{sin {}^{2} \theta + cos {}^{2} \theta = 1}

 \sf{({ \frac{7}{25}}) {}^{2} + cos {}^{2} \theta = 1}

 \sf{cos {}^{2} \theta = 1 - ( \frac{7}{25}) {}^{2}}

 \sf{cos {}^{2} \theta = 1 - \frac{49}{625}}

 \sf{cos {}^{2} \theta = \frac{625 - 49}{625}}

 \sf{cos {}^{2} \theta = \frac{576}{625}}

Taking square roots on both the sides,

 \sf{ \boxed {cos {}^{2} \theta = \frac{24}{25}}}
_____________________________

Now,
 \sf{tan \theta = \frac{sin \theta}{cos \theta}}

 \therefore \sf{tan \theta = \frac{ \frac{7}{25} }{ \frac{24}{25}} }

 \sf{ \therefore \: tan \theta = \frac{7}{25} \times \frac{25}{24}}

 \sf{ \therefore \tan \theta = \frac{7}{{ \cancel 25}} \times \frac{ \cancel25}{24}}

 \sf{ \boxed {\therefore \: tan \theta = \frac{7}{24}}}

Final answer =>

 \sf{cos \theta = \frac{24}{25}}

 {\sf {\tan \theta = \frac{7}{24}}}
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