wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

If α and β are angles in the first quadrant, and tanα=17, sinβ=110, then using the formula sin(A+B)=sinAcosB+cosAsinB, find the value of (α+2β).

A
0
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
45
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
C
60
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
90
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is B 45
we know that, sin2β=2tanβ1+tan2βcos2β=1tan2β1+tan2β

also we know that, 1+tan2α=sec2α1+(17)2=sec2α5049cos2α=4950
cosα=752sinα=14950=152

also, we know that, sinβ=110cosβ=1110=310
tanβ=sinβcosβ=13

Now, sin(α+2β)=sinαcos2β+cosαsin2β=152×1tan2β1+tan2β+752×2tanβ1+tan2β=152[1191+19+7×231+19]=152[810+7×610]=152[5010]=152×5=12sin(α+2β)=12(α+2β)=45o

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Compound Angles
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon