If a = x cosec α sin β, b = y cosec α cos β, and c = z cot α, then find \frac{a^2}{X^2 }+\frac{b ^2}{Y^2}-\frac{c^2}{Z^2} .

SSC CPO SI and ASI Model Paper 8

Question : 105 of 200

Marks: +1, -0

If a = x cosec α sin β, b = y cosec α cos β, and c = z cot α, then find

{a^2}/{X^2 }+{b ^2}/{Y^2}-{c^2}/{Z^2} .

Solution:

{a^2}/{x^2}+ {b^2}/{y^2} -{c^2}/{z^2}

={x^2 cosec^2 α sin^2β}/{x^2}+

{y^2 cosec^2α cos^2β}/{y^2}

-{z ^2cot^2 α}/{z^2}

= cosec^2 α(sin^2 β + cos^2 β) – cot^2 α

= cosec^2 α– cot^2α = 1

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