Question

3 Sin 25° Cos 65° + Cos 25° Sin 65°​

Answer 1

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3 Sin 25° Cos 65° + Cos 25° Sin 65°

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$\longrightarrow$ 1

Step-by-step explanation: $<font \: color=purple >$

$\longrightarrow$ Sin 25° Cos 65° + Cos 25° Sin 65°

$\longrightarrow$ Sin 25° Sin (90° - 65°) + Cos 25° Cos (90° - 65°)

$\longrightarrow$ Sin 25° Sin 25° + Cos 25° Cos 25°

$\longrightarrow$ Sin² 25° + Cos² 25°

$\longrightarrow$ 1 { Sin² A + Cos² A = 1}

Answer 2

sin 25° cos 65° + cos 25° sin 65°

= sin 25° cos (90° – 25°) + cos 25° sin (90° – 25°)

= sin 25° sin 25° + cos 25° + cos 25°

= sin2 25° + cos2 25° = 1.

[∴ cos2 θ + sin2 θ = 1]