Question

If cosec ^6 - cot ^6=a cot^4 + bcot^2+c then a+b+c=


1) 0
2) 7
3) 6
4)1​

Answer 1

Answer: OPTION 2) 7

Step-by-step explanation: HERE IS YOUR EXPLANATION AS IT IS FOR 50 POINTS! :-

We know that, csc2θ=cot2θ+1.......(1).

(csc2θ)3=(cot2θ+1)3.

Since, (x+y)3=x3+y3+3xy(x+y), we have,

csc6θ=(cot2θ)3+13+3(cot2θ)(1)(cot2θ+1),

=cot6θ+1+3cot2θ(csc2θ).......[∵,(1)],                                                                      

HOPE IT HELPS! PLEASE MARK ME AS BRAINLY FOR GIVING CORRECT AND MEANINGUL ANSWER! THANKS FOR THE OPPORTUNITY! ALL THE BEST!:):):):):)

Answer 2

Answer:

Option : 2) 7

cosec^6@-cot^6@

=(cosec^2@)^3-(cot^2)^3

use formula

a^3-b^3= (a-b)^3-3ab(a-b)

=(csc^2@-cot^2@)^3+3(csc^2@)(cot^2@)(csc^2@-cot^2@)

As we know csc^2-cot^2=1

=(1)^3+3(csc^2@)(cot^2@)(1)

=1+3cot^2@(1+cot^2@)

=3cot^4@+3cot^2+1

compare with LHS

a=3 , b=3 , c=1

So,

a+b+c= 7

hence option 2 is correct

soln refers to the attachment