Question

$\sin^{2}{52 \times 1 \div 2} - \sin ^{2} {22 \times 1 \div 2}$
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Answer 1

Answer:

sin74°

Step-by-step explanation:

sin²52° x 1/2 - sin²22° x 1/2

Wkt, cosФ = sin(90-Ф)

        cos²Ф = sin²(90-Ф)

So, sin²52° x 1/2 - sin²22° x 1/2 can be written as

1/2 [ sin²52° - sin²22°]

⇒ 1/2 [ sin(52+22) x sin(52-22) ]              ∵ sin²α - sin²β = sin(α+β)·sin(α-β)

                                                                        [It's like a²-b² = (a+b)(a-b) formula]

⇒ 1/2 [sin74° x sin30°]

⇒ 1/2 [ sin74° x 1/2 ]                                   ∵ sin30° = 1/2

⇒ sin74°

Hope this helped!