If θ = 15/17 then for 0^{}

Correct Answer is : 2349\;\;23/494923

Correct Answer is : 2349\;\;23/494923

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AP ICET 2024 6th May 2024 Shift 1

Question : 163 of 200

Marks: +1, -0

\sin \theta = \frac{15}{17}

0^{\circ} < \theta < 90^{\circ} \; \frac{15 \cot \theta + 17 \sin \theta}{8 \tan \theta + 16 \sec \theta}

Solution:

Given

\sin \;(\theta) = \frac{15}{17}

, we can use the Pythagorean identity

\sin^2(\theta) + \cos^2(\theta) = 1

to find

\cos(\theta)

\cos(\theta) = \sqrt{1 - \sin^2(\theta)} = \sqrt{1 - \left(\frac{15}{17}\right)^2} = \frac{8}{17}.

Now, we can use the values of

\sin (\theta)

and

\cos (\theta)

to calculate the trigonometric functions in the given expression and simplify to get

\;\frac{23}{49}

Quick Tip

Use the identity

\sin^2(\theta) + \cos^2(\theta) = 1

to find unknown trigonometric values and simplify expressions.

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