In ncert class 10 introduction of trigonometry how i solve the exercise 8.4 question number 3(2) easily . Please help me to find the best way to solve this question in a easiest way . Evaluate: (ii) sin 25° cos 65° + cos 25° sin 65°.
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sin 25° cos 65° + cos 25° sin 65°
To simplify this, convert some of the sin functions into cos functions and cos function into sin function and it becomes,
= sin(90°-25°) cos 65° + cos (90°-65°) sin 65°
= cos 65° cos 65° + sin 65° sin 65°
= cos265° + sin265° = 1 (since sin2A + cos2A = 1)
Therefore, sin 25° cos 65° + cos 25° sin 65° = 1