Question

sin 48 cos 42+cos 48 sin 42

Answer 1

Hey !!!

sin48° cos42° + cos48 ° sin42°

sin48° sin(90° -48° ) + cos48° sin( 90° - 48° )

sin48° sin48° + cos48° cos48°

sin²48° + cos²48

=> 1 [•°• sin²¢ + cos²¢ = 1 ]

Answer = 1
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Hope it helps you !!!

@Rajukumar111

Answer 2

[0010001111]... Hello User... [1001010101]
Here's your answer...

Here, we are going to use the complementary angle property of trigonometric ratios.
sin x = cos (90-x) and cos x = sin (90-x)

So sin 42 = sin (90-48) = cos 48
And cos 42 = cos (90-48) = sin 48

Substituting these values in the given equation...
sin 48 × sin 48 + cos 48 × cos 48
= sin² 48 + cos² 48
Another identity... sin²x + cos²x = 1
So sin²48 + cos²48 = 1

Here's another method, just so you know. ^^

If we assume that 48 = A and 42 = B, the above equation becomes
sin A cos B + cos A sin B
This is the formula for sin(A+B)
So, we can directly put A and B's values in sin (A+B) = sin (42+48) = sin 90 = 1.
However, this method only works if you know the values of the trigonometric ratios of the angle you will be ending up with.

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