The numerical value of \frac{\cos^2 60^\circ}{\sin^2 45^\circ}+\frac{\tan^2 30^\circ}{\cot^2 45^\circ}-\frac{\sin^2 30^\circ}{\cot^2 30^\circ}-3/4 is

RRB Junior Engineer Stage 1 Model Papers 8

Question : 24 of 100

Marks: +1, -0

The numerical value of

{\cos^2 60°}/{\sin^2 45°}+{\tan^2 30°}/{\cot^2 45°}-{\sin^2 30°}/{\cot^2 30°}-3/4

Solution:

{\cos^2 45°}/{\sin^2 60°}+{\cos^2 60°}/{\sin 45°}-{\tan^2 30°}/{\cot^2 45°}-{\sin 30°}/{\cot^2 30°}

={(1/√2)^2}/{(√3/2)^2}+{(1/2)^2}/{(1/√2)^2}-{(1/√2)^2}/(1)^2-{(1/2)^2}/(√3)^2

=1/2×4/3+1/4×2/1-1/3-1/4×1/3

⇒2/3+1/2-1/3-1/12

⇒{8+6-4-1}/12=9/12=3/4

Go to Question:

Prev Question

Next Question