Question

If sin A=3/4
then find the value of tan A.
​

Answer 1

$\underline{\boxed{\bold{Question}}}$  

↠ If sin A=3/4  then find the value of tan A.

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$\underline{\boxed{\bold{Important\;Information}}}$  

↠ Complementary angle are angles whose sum is 90°

❏ Here are certain relation of trigonometric functions related to complement of their functions.

       ✧ sinθ = cos(90° - θ)

       ✧ cosθ = sin(90° - θ)

       ✧ tanθ = cot(90° - θ)

       ✧ cotθ = tan(90° - θ)

       ✧ secθ = cosec(90° - θ)

       ✧ cosecθ = sec(90° - θ)

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$\underline{\boxed{\bold{Given}}}$

❏ sinA = 3/4

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$\underline{\boxed{\bold{Answer}}}$

Let's Start !

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➮ There are 2 method for solving this questions !

➮ Lets se then one by one !

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Method : 1

As we are given value of sinA we can find value of cosA by using suitable identity !

$\boxed { \bold { \red { : \leadsto \; sin^{2} \theta + cos^{2} \theta = 1 } } }$

$\bold { \blue{:\implies \; (\frac{3}{4})^{2} + cos^{2} \theta = 1 }}$

$\bold { \red {:\implies \; \frac{9}{16} + cos^{2} \theta = 1 }}$

$\bold { \blue {:\implies \; cos^{2} \theta = 1 - \frac{9}{16} }}$

$\bold { \blue {:\implies \; cos^{2} \theta =\frac{7}{16} }}$

$\boxed { \bold { \orange {:\implies \; cos \theta =\frac{ \sqrt{7}} {4} }}}$

As we know,

$\bold { \pink {:\implies \; tan\theta = \frac{sin \theta}{sin \theta} }}$

$\bold { \green {:\implies \; tan\theta = \frac{\frac{3}{4}}{\frac{\sqrt{7} }{4} } }}$

$\boxed { \bold { \orange {: \implies \; tan\theta = \frac{3}{\sqrt{7} } } } }$

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Method : 2

Let us consider a triangle given in attachment !

BC = 3k

AC = 4k

Now let's apply Pythagoras theorem,

$\boxed { \bold { \red { : \leadsto \; AB^{2} + BC^{2} = AC^{2} } } }$

$\bold { \blue { : \implies \; AB^{2} + (3k)^{2} = (4k)^{2} } }$

$\bold { \red { : \implies \; AB^{2} = 16k^{2} - 9k^{2} } }$

$\bold { \blue { : \implies \; AB^{2} = 7k^{2} } }$

$\boxed{ \bold { \orange { : \implies \; AB = (\sqrt{7})k } } }$

$\bold { \pink {:\implies \; tan\theta = \frac{Opposite \;side}{Adjacent \;side} }}$

$\bold { \orange {:\implies \; tan\theta = \frac{BC}{AB} } }$

$\bold { \green {:\implies \; tan\theta = \frac{3k}{(\sqrt{7})k } }}$

$\boxed { \bold { \purple{:\implies \; tan\theta = \frac{3}{(\sqrt{7}) } } } }$

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$\boxed{\boxed{\bold{\therefore Value \; of \; tan\theta = \frac{3}{(\sqrt{7}) } } } }$

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Hope this helps u.../

【Brainly Advisor】