Question

Only an expert can answer this question of trigonometry and solve this i will mark as brainliest to appropriate answer.
please answer the Question No.18.
hope you can answer my question.

Answer 1

Given, 0 <= A or B  <= 90° (Here alpha=A and beta=B)

So the trigonometric ratios are all positive,  

tan A = 1/7

=> Sec² A = 1 + 1/49 = 50/49     

=>Cos A = 7/√50

=>Sin² A = 1 - 49/50 = 1/50        

=>Sin A = 1/√50

          
=>sin B = 1/√10     

=> Cos² B  = 1 - 1/10 = 9/10     

=> Cos B = 3/√10

Sin (A + B) = Sin A cos B + Cos A Sin B 

= 3/√500  + 7/√500 =  10/√500  =   1/√5

Cos² (A+B) = 1 - 1/5 = 4/5         

=>  Cos (A+B) = 2/√5

Sin (A+B  +  B) = Sin (A+B) Cos B + Cos(A+B) Sin B
                    
= 3/√50 + 2/√50 =  1/√2

A + 2 B = 45°

Answer 2

$\sqrt{\frac{1-\cos x}{1+\cos x}}=\sqrt{\frac{1-1+2\sin^2\frac{x}{2}}{1+2\cos^2\frac{x}{2}-1}}=\sqrt{\frac{\sin^2\frac{x}{2}}{\cos^2\frac{x}{2}}}=\sqrt{\tan^2\frac{x}{2}}=\left|\tan\frac{x}{2}\right|$
and last apply the formula then calculate