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

Prove that:
(i) cos245°-sin215°=34
(ii) sin2 (n + 1) A − sin2 nA = sin (2n + 1) A sin A.

Open in App
Solution

(i)
cos245°-sin215°=cos45°+15°cos45°-15° cos2X-sin2Y=cosX+YcosX-Y=cos60°cos30°=12×32=34

Hence proved.

(ii)
LHS = sin2n+1A - sin2nA =sinn+1A+nA sinn+1A-nA Using the formula sin2X - sin2Y = sinX+Y sinX-Y and taking X = n+1A and Y = nA =sinn+1+nA sin n+1-nA =sin2n +1A sinA = RHSHence proved.

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