R D Sharma Solutions for Chapter: Values of Trigonometric Functions at Sum or Difference of Angles, Exercise 1: EXERCISE 7.1

If $\mathrm{s}\mathrm{i}\mathrm{n}A=\frac{12}{13}$ and $\mathrm{s}\mathrm{i}\mathrm{n}B=\frac{4}{5},$ where $\frac{\pi }{2}<A<\pi$ and $0<B<\frac{\pi }{2}$, find the value of: $\cos \left(A+B\right)$.
 

If  $\sin A=\frac{3}{5}, \cos B=-\frac{12}{13}$, where $A$ and $B$ both lie in second quadrant, find the value of $\sin \left(A+B\right)$.

If $\mathrm{c}\mathrm{o}\mathrm{s}A=-\frac{24}{25}$ and $\mathrm{c}\mathrm{o}\mathrm{s}B=\frac{3}{5}$ , where $\pi <A<\frac{3\pi }{2}$ and $\frac{3\pi }{2}<B<2\pi$, find the following: $\sin \left(A+B\right)$
 

If $\mathrm{c}\mathrm{o}\mathrm{s}A=-\frac{24}{25}$ and $\mathrm{c}\mathrm{o}\mathrm{s}B=\frac{3}{5}$ , where $\pi <A<\frac{3\pi }{2}$ and $\frac{3\pi }{2}<B<2\pi$, find $\cos \left(A+B\right)$.
 

If $\mathrm{t}\mathrm{a}\mathrm{n}A=\frac{3}{4}, \cos B=\frac{9}{41}$,  where $\pi <A<\frac{3\pi }{2}$ and $0<B<\frac{\pi }{2}$, find $\mathrm{t}\mathrm{a}\mathrm{n}(A+B)$.

 If $\sin A=\frac{1}{2}, \cos B=\frac{\sqrt{3}}{2}$, where $\frac{\pi }{2}<A<\pi$  and  $0<B<\frac{\pi }{2}$,  find the value of: $\tan (A+B)$

If $\mathrm{c}\mathrm{o}\mathrm{s}A=-\frac{12}{13}$ and $\mathrm{c}\mathrm{o}\mathrm{t}B=\frac{24}{7}$, where $A$ lies in the second quadrant and $B$ in the third quadrant, find the values of $\mathrm{s}\mathrm{i}\mathrm{n}(A+B)$.

If $\alpha , \beta$ are two different values of $x$ lying between $0$ and $2\pi$ which satisfy the equation $6\cos x+8\sin x=9,$ find the value of $\sin (\alpha +\beta )$.