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) $\frac{\cos {28}^{°}}{\sin {62}^{°}}$

(A) 2 (B) $-$1 (C) 0 (D) 1

Answer 1

(i)
We know, $\sin \theta =\cos \left(90°-\theta \right)$.

Also,

$\cos \theta =\sin \left(90°-\theta \right)$ and $\tan \theta =\cot \left(90°-\theta \right)$

Hence, the correct answer is option (A).

(ii)
We know, sin90º = 1.

Hence, the correct answer is option (D).

(iii)
$$\begin{gathered} 2\tan 45°+\cos 45°-\sin 45° \\ =2\times 1+\frac{1}{\sqrt{2}}-\frac{1}{\sqrt{2}} \\ =2 \end{gathered}$$
Hence, the correct answer is option (C).

(iv)
$$\begin{gathered} \frac{\cos 28°}{\sin 62°} \\ =\frac{{\displaystyle \sin \left(90°-28°\right)}}{{\displaystyle \sin 62°}}\left[\cos \theta =\sin \left(90°-\theta \right)\right] \\ =\frac{{\displaystyle \sin 62°}}{{\displaystyle \sin 62°}} \\ =1 \end{gathered}$$
Hence, the correct answer is option (D).