# If α and β are the angles in the first quadrant tan α=1/7 sin β=1/√10 then using the formula sin(α β)=sinα cosβ cosα sinβ find the value of α+2β

1
by jessyjose1225

2015-09-21T13:48:22+05:30

### This Is a Certified Answer

Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest.
given  0 <= A or B  <= 90°.  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°
================================================
You may also find the value of  Sin 2B,  Cos 2B  using their formulas.
then  find  Sin  (A+2B ).

Sin 2B = 6/10 = 3/5            Cos2B = 9/10 - 1/10 = 4/5

So Sin(A+2B) = 1/√50 * 4/5  + 3/5 * 7/√50
= 1/√2
So A + 2B = 45 deg.

click on thanksb utton above pls