SINA+SIN3A+SIN5A+SIN7A
SINA+SIN3A+SIN5A+SIN7A
MANIDEEP , 10 Years ago
Grade 11
Trigonometry> SINA+SIN3A+SIN5A+SIN7A...
3 Answers
Athiyaman
Hey Manideep,
the answer should be 16 sinA.cos22A.cos2A
you will have to use these 3 formulas in order to get the answer:
1)sinA+sinB=2sin(A+B)/2.cos(A-B)/2
2)cosA+cosB=2cos(A+B)/2.cos(A-B)/2 and lastly,
3)sin2A=2sinA.cosA
Athiyaman
And if you want the answer here it is:
sinA + sin5A + sin3A + sin7A
= (sinA + sin7A) + (sin5A + sin3A)
= (sinA + sin7A) + (sin5A + sin3A)
After rearranging the terms use identity 1 from the above post,
= 2 sin 4A cos 3A + 2 sin 4A cos A
= 2 sin 4A cos 3A + 2 sin 4A cos A
Here 2sin4A is common
=2 sin 4A [ cos 3A + cos A ]
Use Identity 2 from the above post,
=2 sin 4A * 2 cos 2A cos A
=2 sin 4A [ cos 3A + cos A ]
Use Identity 2 from the above post,
=2 sin 4A * 2 cos 2A cos A
sin4A can be split into 2sin2A.cos2A from identity 3,
= 4 sin 2A cos 2A * 2 cos 2A cos A
= 4 sin 2A cos 2A * 2 cos 2A cos A
Again use sin2A formula
= 8 sin A * cos A *cos 2A * 2 cos 2A cos A
= 8 sin A * cos A *cos 2A * 2 cos 2A cos A
and then just arrange the terms
= 16 sin A cos² A * cos² (2A)
= 16 sin A cos² A * cos² (2A)
Please approve the answer if you found it helpful
Lab Bhattacharjee
http://www.askiitians.com/forums/Trigonometry/sina-sin3a-sin5a-sin7a_125330.htm
LIVE ONLINE CLASSES
Prepraring for the competition made easy just by live online class.
Full Live Access
Study Material
Live Doubts Solving
Daily Class Assignments
Other Related Questions on trigonometry
In ABC, if cot A+cot B+cot C = cosecA cosecB cosecC, then prove that ABC is right angle triangle.
In ABC, if cot A+cot B+cot C = cosecA cosecB cosecC, then prove that ABC is right angle triangle.
trigonometry
1 Answer Available
Last Activity: 3 Years ago
- Find the general solution of equation tan3∂=cot2∂
For all angles between -720 and +720
- Find the general solution of equation tan3∂=cot2∂
For all angles between -720 and +720
trigonometry
1 Answer Available
Last Activity: 3 Years ago
To prove : Cosec(45 degree - A)Cosec(45 degree + A) = 2SecA
To prove : Cosec(45 degree - A)Cosec(45 degree + A) = 2SecA
trigonometry
1 Answer Available
Last Activity: 3 Years ago
Derive a formula for the area of the triangle, given b, A, B, and C. That is, derive the formula: (b^2sinAsinC)/(2sinB)
Derive a formula for the area of the triangle, given b, A, B, and C. That is, derive the formula: (b^2sinAsinC)/(2sinB)
trigonometry
1 Answer Available
Last Activity: 3 Years ago
WHAT IS THE LIMIT WHEN X TOWARDS TO 0 OF sin6x/5x ? lim𝑥→0 𝑠𝑖𝑛6𝑥/5𝑥
WHAT IS THE LIMIT WHEN X TOWARDS TO 0 OF sin6x/5x ? lim𝑥→0 𝑠𝑖𝑛6𝑥/5𝑥
trigonometry
1 Answer Available
Last Activity: 3 Years ago