a) 2 sin 70° cos 30° express the following as sum or difference of trigonometric function About the author Aubrey
Step-by-step explanation: Consider the equation, Case 1- 2sin4θcos2θ sinA+sinB=2sin( 2 A+B )cos( 2 A−B ) =2sin( 2 6θ+2θ )cos( 2 6θ−2θ ) =2sin4θcos2θ Case 2- 2sin2θcos4θ sinA+sinB=2sin( 2 A+B )cos( 2 A−B ) =2cos( 2 6θ+2θ )sin( 2 6θ−2θ ) Case 3- 2sin2θsin4θ cosA−cosB=−2sin( 2 A+B )sin( 2 A−B ) =−2sin( 2 6θ+4θ )sin( 2 6θ−2θ ) =2sin2θsin4θ Case 4-2cos2θcos4θ cosA−cosB=2cos( 2 A+B )cos( 2 A−B ) =2cos( 2 6θ+4θ )cos( 2 6θ−4θ ) =2cos2θcos4θ Hence, Proved. Hope this will help you Mark me as brilliant Reply
Step-by-step explanation:
Consider the equation,
Case 1- 2sin4θcos2θ
sinA+sinB=2sin(
2
A+B
)cos(
2
A−B
)
=2sin(
2
6θ+2θ
)cos(
2
6θ−2θ
)
=2sin4θcos2θ
Case 2- 2sin2θcos4θ
sinA+sinB=2sin(
2
A+B
)cos(
2
A−B
)
=2cos(
2
6θ+2θ
)sin(
2
6θ−2θ
)
Case 3- 2sin2θsin4θ
cosA−cosB=−2sin(
2
A+B
)sin(
2
A−B
)
=−2sin(
2
6θ+4θ
)sin(
2
6θ−2θ
)
=2sin2θsin4θ
Case 4-2cos2θcos4θ
cosA−cosB=2cos(
2
A+B
)cos(
2
A−B
)
=2cos(
2
6θ+4θ
)cos(
2
6θ−4θ
)
=2cos2θcos4θ
Hence, Proved.
Hope this will help you
Mark me as brilliant