Question

If cosec x + cot x = a, then the value of cos x is
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Answer 1

Answer:

cosec x +cot x = a --------------(1)

we know that

cosec^2 x -cot^2 x = 1

(cosec x +cot x)(cosec x -cot x) = 1

a(cosec x-cot x) = 1

(cosec x-cot x) = 1/a ------------------(2)

from (1) & (2)

cosec x+cot x = a

cosec x-cot x = 1/a

2cosec x = a+1/a

2cosec x= a^2+1/a

cosec x = a^2+1/2a

sin x = 2a/a^2+1

we know that

cos x = √1-sin^2 x

cos x = √1-[2a/a^2+1]^2

cos x = √1-4a^2/(a^2+1)^2

cos x = √(a^2+1)^2-4a^2/(a^2+1)^2

cos x = √(a^2-1)^2/(a^2+1)^2 {·(a+b)^2-(a-b)^2 = 4ab}

cos x = √[a^2-1/a^2+1]^2

Step-by-step explanation:

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