Question
Download Solution PDFIf sin x =
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
sin x =
Formula Used:
sin(x + y) = sin x cos y + cos x sin y
sin2x + cos2x = 1
Calculation:
We know that,
sin2x + cos2x = 1
⇒
⇒
⇒ cos2x =
⇒ cos2x =
⇒ cos x =
⇒ cos x =
Since x in IInd quadrant.
So, cos x is negative.
⇒ cos x =
⇒ sin2y + cos2y = 1
⇒ sin2y = 1 - cos2y
⇒ sin2y =
⇒ sin2y =
⇒ sin2y =
⇒ sin y =
⇒ sin y =
Since y lies in IInd quadrant,
So, sin y is positive.
⇒ sin y =
Now, Putting the values of sin x, cos x, sin y, cos y
⇒ sin (x + y) = sin x cos y + cos x sin y
⇒ sin (x + y) =
⇒ sin (x + y) =
⇒ sin (x + y) =
⇒ sin (x + y) =
∴ The value of sin(x + y) is
Last updated on Jun 19, 2025
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