Let sinx + siny = a and cosx + cosy = b. Then sin(x+y) is equal to

a)      ab/(a+b)

b)      ab/(a²+b²)

c)      2ab/(a²+b²)

d)      ab/2(a²+b²)

Question

Let sinx + siny = a and cosx + cosy = b. Then sin(x+y) is equal to a) ab/(a+b) b) ab/(a 2 +b 2 ) c) 2ab/(a 2 +b 2 ) d) ab/2(a 2 +b 2 )

vikas askiitian expert · Answer

sinx + siny = a

2sin(x+y/2)cos(x-y/2) = a ......................1 (by using sum formula)

cosx + cosy = b

2cos(x-y/2)cos(x+y/2) = b ..................2

divide both

tan(x+y/2) = a/b ...........3

tan²@ = sec²@ - 1 & sec@ = 1/cos@ so

cos(x+y/2) = [b²/a²+b²]^1/2......................4

sin(x+y/2) = {1-cos²(x+y/2)}^1/2 = [a²/a²+b²]^1/2.............5

sinx+y = 2sin(x+y/2)cos(x+y/2) (sinA = 2sinA/2cosA/2)

from eq 4 & 5

sinx+y = 2ab/a²+b²

option c is correct

Thank you for registering.

Register Now and Win Upto 25% Scholorship for a Full Academic Year !

Enter Your Details

Registration done!

Let sinx + siny = a and cosx + cosy = b. Then sin(x+y) is equal to a) ab/(a+b) b) ab/(a 2 +b 2 ) c) 2ab/(a 2 +b 2 ) d) ab/2(a 2 +b 2 )

Let sinx + siny = a and cosx + cosy = b. Then sin(x+y) is equal to

a)      ab/(a+b)

b)      ab/(a²+b²)

c)      2ab/(a²+b²)

d)      ab/2(a²+b²)

1 Answers

Think You Can Provide A Better Answer ?

Provide a better Answer & Earn Cool Goodies See our forum point policy

Other Related Questions on Trigonometry

ASK QUESTION

Answer and earn gift vouchers

View courses by askIITians

Design classes One-on-One in your own way with Top IITians/Medical Professionals

Complete Self Study Package designed by Industry Leading Experts

Live 1-1 coding classes to unleash the Creator in your Child

a Complete All-in-One Study package Fully Loaded inside a Tablet!

Register Now & Win Upto 25% Scholorship

Thank you for registering.

Register Now and Win Upto 25% Scholorship for a Full Academic Year !

Enter Your Details

Registration done!

Let sinx + siny = a and cosx + cosy = b. Then sin(x+y) is equal to a) ab/(a+b) b) ab/(a 2 +b 2 ) c) 2ab/(a 2 +b 2 ) d) ab/2(a 2 +b 2 )

Let sinx + siny = a and cosx + cosy = b. Then sin(x+y) is equal to a) ab/(a+b) b) ab/(a2+b2) c) 2ab/(a2+b2) d) ab/2(a2+b2)

1 Answers

Think You Can Provide A Better Answer ?

Provide a better Answer & Earn Cool Goodies See our forum point policy

Other Related Questions on Trigonometry

ASK QUESTION

Answer and earn gift vouchers

View courses by askIITians

Design classes One-on-One in your own way with Top IITians/Medical Professionals

Complete Self Study Package designed by Industry Leading Experts

Live 1-1 coding classes to unleash the Creator in your Child

a Complete All-in-One Study package Fully Loaded inside a Tablet!

Register Now & Win Upto 25% Scholorship

Let sinx + siny = a and cosx + cosy = b. Then sin(x+y) is equal to

a) ab/(a+b)

b) ab/(a²+b²)

c) 2ab/(a²+b²)

d) ab/2(a²+b²)