Question

tan²(1/2cos⁻¹ 2/3), Evaluate it.

Answer 1

we have to find the value of tan²{1/2cos^-1(2/3)}

Let 1/2cos^-1(2/3) = A ..........(1)

cos^-1(2/3) = 2A

cos2A = 2/3

we know, cos2A = (1 - tan²A)/(1 + tan²A)

2/3 = (1 - tan²A)/(1 + tan²A)

2(1 + tan²A) = 3(1 - tan²A)

2 + 2tan²A = 3 - 3tan²A

5tan²A = 3 - 2 = 1

tan²A = 1/5 .......(2)

from equations (1) and (2),
tan²{1/2cos^-1(2/3)} = tan²A = 1/5

Answer 2

Answer:

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