how to eliminate theta...(d given angles)

eliminate θ and φ if sinθ+sinφ=a , cosθ+cosφ=b and tan(θ/2)tan(φ/2)=c

the way i tried to solve this ques...has made the solution complex...

8 Answers

62
Lokesh Verma ·

cant think of a simple soln right away.. but seems interesting..

can ewe try to introduce complex nos?

eiφ + eiθ = a+ib b+ai (edited)

I am not sure.. but can this help? just thinking!

1
rupal jain ·

thanx..i'll try to solve by ur method...

1
Rohan Ghosh ·

actually i got another easier way!!

take cosθ=x and cosφ=y

then x+y =

also

tanθ/2tanφ/2=c
hence

(sinθ/2sinφ/2)/(cosφ/2cosθ/2)=c

multiplying both numerator and denominator with 4cosθ/2cosφ/2

we get

(sinθsinφ)/(2cos2θ/2)*(2cos2φ/2)=c

replacing 2cos2θ/2 by cosθ+1 and similarly the other

we get the expression (i)

now square the first equation and the second equation and add them

you will get the relation between
sinθsinφ and cosθcosφ

thus you can write expression (i) in terms of cosθ and cosφ

thus you have two equations and two variables!!

1
challenger ·

nishant i suppose it should be b+ia

62
Lokesh Verma ·

yes.. u are right dear.. (bhawna ko samjho :) :D

62
Lokesh Verma ·

but yeah.. thanks for poiting out.. i corrected it :)

33
Abhishek Priyam ·

haan bhavnao ko samajhna chahiye...

are ye to maine kaha tha to Vyom :P

62
Lokesh Verma ·

haha.. :D

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