Question

Fill in the blanks.
(i) $\sin {20}^{\circ }=\cos$____${}^{\circ }$
(ii) $\tan {30}^{\circ }\times \tan$___${}^{\circ }=1$
(iii) $\cos {40}^{\circ }=\sin$____${}^{\circ }$

Answer 1

(i) $\sin {20}^{\circ }=\cos ({90}^{\circ }-{20}^{\circ })=\cos {\underset{–}{70}}^{\circ }$ [$\because \sin \theta =\cos ({90}^{\circ }-\theta )$]
(ii) $\tan {30}^{\circ }=\frac{1}{\sqrt{3}}\dots \dots \left(i\right)$

$\tan {60}^{\circ }=\sqrt{3}\dots \dots \left(ii\right)$

On multiplying eq.(i) and (ii), we get

$\tan {30}^{\circ }\times \tan {\underset{–}{60}}^{\circ }=1$

(iii) $\cos {40}^{\circ }=\sin ({90}^{\circ }-{40}^{\circ })=\sin {\underset{–}{50}}^{\circ }$ [$\because \cos \theta =\sin {90}^{\circ }-\theta$]