====== Question 1, Review Exercise 10 ======

Solutions of Question 1 of Review Exercise 10 of Unit 10: Trigonometric Identities of Sum and Difference of Angles. This is unit of A Textbook of Mathematics for Grade XI is published by Khyber Pakhtunkhwa Textbook Board (KPTB or KPTBB) Peshawar, Pakistan.

===== Question 1 =====
 Chose the correct option.

i.  $\cos {{50}^{\circ }}5{0}'\cos {{9}^{\circ }}1{0}'-\sin {{50}^{\circ }}5{0}'\sin {{9}^{\circ }}1{0}'=$
    * (a) $0$  
    * (b) $\dfrac{1}{2}$
    * %%(c)%% $1$
    * (d) $\dfrac{\sqrt{3}}{2}$ \\ <btn type="link" collapse="a1">See Answer</btn><collapse id="a1" collapsed="true">(B): $\dfrac{1}{2}$</collapse>

ii. If $\tan {{15}^{\circ }}=2-\sqrt{3}$, then the value of  ${{\cot }^{2}}{{75}^{\circ }}$ is  
    * (a) $7+\sqrt{3}$  
    * (b) $7-2\sqrt{3}$
    * %%(c)%% $7-4\sqrt{3}$
    * (d) $7+4\sqrt{3}$ \\ <btn type="link" collapse="a2">See Answer</btn><collapse id="a2" collapsed="true">(B): $\dfrac{1}{2}$</collapse>

iii. If $\tan \left( \alpha +\beta  \right)=\dfrac{1}{2}$, and $\tan \alpha =\dfrac{1}{3}$ then $\tan \beta =$  
    * (a) $\dfrac{1}{6}$ 
    * (b) $\dfrac{1}{7}$
    * %%(c)%% $1$
    * (d) $\dfrac{7}{6}$ \\ <btn type="link" collapse="a3">See Answer</btn><collapse id="a3" collapsed="true">(B): $\dfrac{1}{2}$</collapse>

iv. $\sin \theta \cos \left( {{90}^{\circ }}-\theta  \right)+\cos \theta \sin \left( {{90}^{\circ }}-\theta  \right)=$  
    * (a) $-1$ 
    * (b) $2$
    * %%(c)%% $0$
    * (d) $1$ \\ <btn type="link" collapse="a4">See Answer</btn><collapse id="a4" collapsed="true">(B): $\dfrac{1}{2}$</collapse>

v. Simplified expression of $\left( \sec \theta +\tan \theta  \right)\left( 1-\sin \theta  \right)$ is  
    * (a) ${{\sin }^{2}}\theta$ 
    * (b) ${{\cos }^{2}}\theta$ 
    * %%(c)%% $ta{{n}^{2}}\theta$
    * (d) $\cos \theta$ \\ <btn type="link" collapse="a5">See Answer</btn><collapse id="a5" collapsed="true">(B): $\dfrac{1}{2}$</collapse>

vi. $\sin \left( x-\frac{\pi }{2} \right)=$ is  
    * (a) $\sin x$  
    * (b) $-\sin x$ 
    * %%(c)%% $\cos x$
    * (d) $-\cos x$ \\ <btn type="link" collapse="a6">See Answer</btn><collapse id="a6" collapsed="true">(B): $\dfrac{1}{2}$</collapse>

vii. A point is in Quadrant-III and on the unit circle. If its x-coordinate is $-\dfrac{4}{5},$ what is the y-coordinate of the point? 
    * (a) $\dfrac{3}{5}$  
    * (b) $-\dfrac{3}{5}$ 
    * %%(c)%% $-\dfrac{2}{5}$
    * (d) $\dfrac{5}{3}$ \\ <btn type="link" collapse="a7">See Answer</btn><collapse id="a7" collapsed="true">(B): $\dfrac{1}{2}$</collapse>

viii. Which of the following is an identity? 
    * (a) $\sin \left( a \right)\cos \left( a \right)=\left( \dfrac{1}{2} \right)\left( \sin 2a \right)$  
    * (b) $\sin a+\cos a=1$ 
    * %%(c)%% $\sin \left( -a \right)=\sin a$
    * (d) $\tan a=\dfrac{\cos a}{\sin a}$ \\ <btn type="link" collapse="a8">See Answer</btn><collapse id="a8" collapsed="true">(a): $\sin \left( a \right)\cos \left( a \right)=\left( \dfrac{1}{2} \right)\left( \sin 2a \right)$  </collapse>

===Go to===
<text align="right"><btn type="success">[[math-11-kpk:sol:unit10:re-ex10-p2|Question 2 & 3 >]]</btn></text>