Question

answer the 1st question ​

Answer 1

Question:

   

If  $\sec\theta+\tan\theta=3$,  find the value of  $\sin\theta$.

Answer: 4/5

   

   

Step-by-step explanation:

             

$\Rightarrow\ \sec^2\theta-\tan^2\theta=1 \\ \\ \Rightarrow\ (\sec\theta+\tan\theta)(\sec\theta-\tan\theta)=1 \\ \\ \Rightarrow\ 3(\sec\theta-\tan\theta)=1 \\ \\ \Rightarrow\ \sec\theta-\tan\theta=\frac{1}{3} \\ \\ \\ \Rightarrow\ (\sec\theta+\tan\theta)+(\sec\theta-\tan\theta)=3+\frac{1}{3} \\ \\ \Rightarrow\ 2\sec\theta=\frac{10}{3} \\ \\ \Rightarrow\ \sec\theta=\frac{5}{3} \\ \\ \\ \Rightarrow\ \cos\theta=\frac{3}{5}$

$\Rightarrow\ (\sec\theta+\tan\theta)-(\sec\theta-\tan\theta)=3-\frac{1}{3} \\ \\ \Rightarrow\ 2\tan\theta=\frac{8}{3} \\ \\ \Rightarrow\ \tan\theta=\frac{4}{3}$

$\Rightarrow\ \sin\theta = \cos\theta \cdot \tan\theta \\ \\ \Rightarrow\ \sin\theta= \frac{3}{5} \cdot \frac{4}{3} \\ \\ \Rightarrow\ \sin\theta=\bold{\frac{4}{5}}$

Thank you. :-))