1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

# Choose the correct alternative answer for following multiple choice questions. (i) Which of the following statements is true ? (A) sin $\mathrm{\theta }$ = cos (90$-$ $\mathrm{\theta }$) (B) cos $\mathrm{\theta }$ = tan (90$-$$\mathrm{\theta }$ ) (C) sin $\mathrm{\theta }$ = tan (90$-$$\mathrm{\theta }$) (D) tan $\mathrm{\theta }$ = tan (90$-$​$\mathrm{\theta }$) (ii) Which of the following is the value of sin 90° ? (A) $\frac{\sqrt{3}}{2}$ (B) 0 (C) $\frac{1}{2}$ (D) 1 (iii) 2 tan 45° + cos 45° $-$ sin 45° = ? (A) 0 (B) 1 (C) 2 ( D) 3 (iv) $\frac{\mathrm{cos}{28}^{°}}{\mathrm{sin}{62}^{°}}$ (A) 2 (B) $-$1 (C) 0 (D) 1

Open in App
Solution

## (i) We know, $\mathrm{sin}\theta =\mathrm{cos}\left(90°-\theta \right)$. Also, $\mathrm{cos}\theta =\mathrm{sin}\left(90°-\theta \right)$ and $\mathrm{tan}\theta =\mathrm{cot}\left(90°-\theta \right)$ Hence, the correct answer is option (A). (ii) We know, sin90º = 1. Hence, the correct answer is option (D). (iii) $2\mathrm{tan}45°+\mathrm{cos}45°-\mathrm{sin}45°\phantom{\rule{0ex}{0ex}}=2×1+\frac{1}{\sqrt{2}}-\frac{1}{\sqrt{2}}\phantom{\rule{0ex}{0ex}}=2$ Hence, the correct answer is option (C). (iv) $\frac{\mathrm{cos}28°}{\mathrm{sin}62°}\phantom{\rule{0ex}{0ex}}=\frac{\mathrm{sin}\left(90°-28°\right)}{\mathrm{sin}62°}\left[\mathrm{cos}\theta =\mathrm{sin}\left(90°-\theta \right)\right]\phantom{\rule{0ex}{0ex}}=\frac{\mathrm{sin}62°}{\mathrm{sin}62°}\phantom{\rule{0ex}{0ex}}=1$ Hence, the correct answer is option (D).

Suggest Corrections
5
Join BYJU'S Learning Program
Related Videos
Trigonometric Ratios of Allied Angles
MATHEMATICS
Watch in App
Join BYJU'S Learning Program