Question

If (1+4x^2)cosA=4x,then find the value of cosecA +cotA​

Answer 1

Step-by-step explanation:

If 4x secA=1+4x², then what is the value of secA+tanA?

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The answer will be 2x..

First of all find the secA from the given condition.

Then just reverse it, you will get the cosA value

Then use the identity sin^2(A) +cos^2(A) =1

Then find the value of sinA from this identity.

Then by using comman Relationship between sinA, cosA and tanA ,find the value of tanA

And then put the values of both secA and tanA in the equation you will get your answer which is equal to 2x..

:)

sec A = (1+4x2)/4x ——→ eq(1)

1 + tan2A = sec2A

tan A = sec2A−1−−−−−−−−√ = [(1+4x2)2/16x2]−1−−−−−−−−−−−−−−−−−√

tanA=[(1+16x4+8x2)/16x2]−1−−−−−−−−−−−−−−−−−−−−−−√=(1+16x4−8x2)/16x2−−−−−−−−−−−−−−−−−−√ ——-> eq(2)

secA+tanA=[(1+4x2)/4x]+(1+16x4−8x2)/16x2−−−−−−−−−−−−−−−−−−√

secA+tanA=[(1+4x2)/4x]+([1−4x2)]2/[4x]2−−−−−−−−−−−−−−√

secA+tanA=[(1+4x2)/4x]+[(1−4x2)/4x]

secA+tanA=[(1+4x2+1−4x2)/4x]

Hence, secA+tanA=1/2x

Answer 2

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