Question

If cos theta is equal to root 3/2 and angle theta is acute angle then sin square theta + tan square theta is equal to

Answer 1

Answer:

7/12

Step-by-step explanation:

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Answer 2

Answer:

$\frac{7}{12}$

Step-by-step explanation:

Given:- cos θ = $\frac{\sqrt{3} }{2}$

To Find:- Value of $sin^{2}$ θ + $tan^{2}$ θ.

Solution:-

Acc. to the question, θ is an acute angle which means θ must be less than 90°.

As, cos θ = $\frac{\sqrt{3} }{2}$

∴ θ = 30°

Then the value of  $sin^{2}$ θ + $tan^{2}$ θ becomes,

      = $(\frac{1}{2}) ^{2} + (\frac{1}{\sqrt{3} }) ^{2}$

      = $\frac{1}{4} + \frac{1}{3}$

      = $\frac{3 + 4}{12}$

      = $\frac{7}{12}$

Hence, the value of  $sin^{2}$ θ + $tan^{2}$ θ is  $\frac{7}{12}$.

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