Question

(2sinx+3cosx)²+(3sinx-2cosx)²=13 prove plz

Answer 1

Answer:

LHS:-

(4sin²x +9cos²x + 12sinxcosx) +(9sin²x+ 4 cos²x -12sinxcosx)

13 (sin²x + cos²x)

13*1 =

13

RHS

HP

Answer 2

Answer:

see explanation

Step-by-step explanation:

Using the identity

sin²x + cos²x = 1

Consider left side

(2sinx + 3cosx)² + (3sinx - 2cosx)² ← expand parenthesis using FOIL

= 4sin²x + 12sinxcosx + 9cos²x + 9sin²x - 12sinxcosx + 4cos²x

Collect like terms

= 13sin²x + 13cos²x ← factor out 13 from each term

= 13(sin²x + cos²x)

= 13 × 1

= 13

= right side , thus proven