Question

Plz help me 2 sort out Q.29 & 30​

Answer 1

= 3+13+21+15+5+4+2/7

=63/7

= 7

Answer 2

Step-by-step explanation:

30.

sin theta + sin^2 theta = 1

sin theta = 1- sin^2 theta

[Identity: sin^2 theta + cos^2 theta = 1; hence 1- sin^2 theta = cos^2 theta]

sin theta = cos^2 theta ....(i)

cos^12 theta + 3 cos^10 theta + 3 cos^8 theta + cos^6 theta + 2 cos^4 theta + 2 cos^2 theta - 2 =

Substitute for cos theta in terms of sin theta as per eq.(i)

sin^6 theta + 3 sin^5 theta + 3 sin^4 theta + sin^3 theta + 2 sin^2 theta + 2 sin theta - 2 =

sin^6 theta + 3 sin^5 theta + 3 sin^4 theta + sin^3 theta + 2(sin^2 theta + sin theta) - 2 =

[sin^2 theta + sin theta = 1]...Given

sin^6 theta + 3 sin^5 theta + 3 sin^4 theta + sin^3 theta + 2 - 2 =

sin^6 theta + 3 sin^3 theta(sin^2 theta +  sin theta) + sin^3 theta =

sin^6 theta + 3 sin^2 theta*sin theta (sin^2 theta + sin theta) + sin^3 theta

[This is of the form: (a+b)^3 = a^3 + 3*a*b(a+b) + b^3]

a = sin^2 theta && b = sin theta

[sin^2 theta + sin theta]^3 = 1^3 = 1

Hence answer is '1'