Question

please solve question no. 19,21(i),(ii) and (iii) ASAP




But if you don't know it's answer then don't answer this question so that someone who know it's answer can answer it​

Answer 1

Answer:

21(ii) Tn = sin^n x+ cos ^nx

T4= sin^4x + cos^4x

T6 = sin^6x + cos^6x

2T_6 -3T_4+10

= 2(sin^6x+cos ^6)-3(sin^4x+ cos ^4x)+10

= 2{(sin^2x)^3+(cos ^2x)^3}- 3{(sin^2x)^2+(cos^2x)^2}+10

[a^3+b^3=(a+b)(a^2-ab+b^2)

a^2+b^2 = (a+b)^2-2ab & sin^2 theta + cos^2 theta= 1]

using these

= 2[(sin^2x+cos^2x)(sin^4x+cos^4x-sin^2x cos^2x)3sin^4x- 3cos^4x+10

= 2sin^4x+2cos^4x-2sin^2x cos^2x - 3sin^4x - 3cos^4x+10

= - sin^4x - cos^4x -2sin^2x cos^2x+10

= 10-[(sin^2x)^2+(cos^2x)^2+2sin^2x cos ^2x]

=10-(sin^2x+cos^2x)^2

=10 - 1 =9