If x/ y=n, x/ y=m, then what is (m² - n²) ² y equal to?

Correct Answer is : 1−n21 - n²1−n2

Correct Answer is : 1−n21 - n²1−n2

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Trigonometry Practice Test 1

Question : 1 of 40

Marks: +1, -0

\frac{\cos x}{\cos y}=n,\frac{\sin x}{\sin y}=m,

(m^2 - n^2) \sin^2 y

equal to?

Solution: 👈: Video Solution

Concept:

Use the given ratios and the identity

\sin^2 x + \cos^2 x = 1

to simplify the expression.

Explanation:

Given:

\frac{\cos x}{\cos y}=n

and

\frac{\sin x}{\sin y}=m

So,

n^2 = \frac{\cos^2 x}{\cos^2 y}

and

m^2 = \frac{\sin^2 x}{\sin^2 y}

Now,

(m^2 - n^2)\sin^2 y

= \left(\frac{\sin^2 x}{\sin^2 y} - \frac{\cos^2 x}{\cos^2 y}\right)\sin^2 y

= \sin^2 x - \frac{\cos^2 x \sin^2 y}{\cos^2 y}

= \frac{(1-\cos^2 x)\cos^2 y - \cos^2 x(1-\cos^2 y)}{\cos^2 y}

= \frac{\cos^2 y - \cos^2 x}{\cos^2 y}

= 1 - \frac{\cos^2 x}{\cos^2 y}

= 1 - n^2

Answer:

(m^2 - n^2)\sin^2 y = 1 - n^2

, so option A is correct.

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