# (solved)Question 7 SSC-CGL 2019 June 13 Shift 1

The value of $\displaystyle \sin^2 32\degree +$ $\displaystyle\sin^2 58\degree -$ $\displaystyle \sin 30\degree +$ $\displaystyle \sec^2 60\degree$ is equal to?
(Rev. 18-Jun-2024)

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### Question 7SSC-CGL 2019 June 13 Shift 1

The value of $\displaystyle \sin^2 32\degree +$ $\displaystyle\sin^2 58\degree -$ $\displaystyle \sin 30\degree +$ $\displaystyle \sec^2 60\degree$ is equal to?

1. 5.5
2. 3.5
3. 4.5
4. 4.0

### Solution in Short

sin 32° is same as cos (90 - 32) = cos 58°. So, the first two terms (cos² 58° + sin² 58°) add to 1. For the next two terms use sin 30° = 1/2 and sec 60° = 2, to get: 1 - (1/2) + 2² = 4.5 answer!

### Solution in Detail

$\displaystyle \sin 32\degree = \cos (90 - 32) = \cos 58 \degree$

The first two terms become

$\displaystyle (\cos^2 58\degree + \sin^2 58\degree) = 1 \text{. . . (1)}$

The third term is $\displaystyle \sin 30\degree = \frac12 \text{. . . (2)}$

The last term is $\displaystyle \sec^2 60\degree = 2^2 \text{. . . (3)}$

Combining (1), (2) and (3)

$\displaystyle 1 - \frac12 + 4 = 4.5 \: \underline{\text{Ans}}$