Question

If (2sin theta + 3cos theta =2, prove that (3 sin theta-2 cos theta)=+-3

Answer 1

Answer:

3sin∅ - 2cos∅ = ±3

Step-by-step explanation:

Given 2sin∅ + 3cos∅ = 2,

To prove that 3sin∅ - 2cos∅ = ±3.

Let us consider value of 3sin∅ - 2cos∅ to be 'x'

Now consider ( 2sin∅ + 3cos∅)² + (3sin∅ - 2cos∅)²

=(4sin²∅ + 9cos²∅ + 12sin∅cos∅) + (9sin²∅ + 4cos²∅ - 12sin∅cos∅)

=13sin²∅ + 13cos²∅

=13(sin²∅ + cos²∅),

We know from trignometric identities, that

sin²∅ + cos²∅ = 1

=> x² + 2² = 13

=>x² = 9

=> x = ±3.

Hence 3sin∅ - 2cos∅ = ±3.

Answer 2

ANSWER:-

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