Question

1. Evaluate without using trigonometric tables,
sin2 28° + sin2 62° + tan2 38° - cot2 52°
+ 1/4 sec2 30°.

Plzzz, ans fast......!!!​

Answer 1

Answer is 4/3.

cos(90-A)=sinA

Therefore sin^2 28 can be written as cos^2 62

(90-28=62)

Therefore the expression becomes cos^2 62+sin^2 62 +tan^2 38 -cot^2 52

(Also cos^2 A+sin^2 A =1)

Therefore equation becomes 1 + tan^2 38 - cot^2 62.

Similarly tan(90-A)=cotA

Therefore tan^2 38= cot^2(90-38)=cot^2 62.

Now the expression is 1 + cot^2 62-cot^2 62 +1/4sec^2 30.

=> 1+1/4 sec^2 30

=>1+1/3[Since sec 30=2/square root(3) sec^2 30=4/3

1/4*sec ^2 30=(1/4)*(4/3)=1/3.]

=>4/3.