Question

Cos theta=√3/2 and theta is acute , find sin^2+tan^2

Answer 1

cosA = √3/2

squaring both sides

cos^2A = 3/4

sin^2A + tan^2A

sin^2A + sin^2A/cos^2A

(sin^2A cos^2A + sin^2A) / cos^2A

change sin^2A into 1-cos^2A

{cos^2A(1-cos^2A) + (1-cos^2A) } /cos^2A

put the value cos^2A = 3/4

{3/4(1 - 3/4) + (1 - 3/4) } / (3/4)

{3/4 (1/4) + (1/4)} / (3/4)

(3/16 + 1/4) / (3/4)

{(3 + 4)/16} / (3/4)

(7/16) / (3/4)

7/16 × 4/3

= 7/12