If sin m + sin n = p, cos m + cos n = q, then find the value of sin m × sin n + cos m ×cos n.
Answer & explanation
Correct answer: option 2
sin m + sin n = p
On squaring both side,
( sin m + sin n )² = p²
sin² m + sin² n + 2 × sin m × sin n = P² ----(1)
And cos m + cos n = q
On squaring both side,
( cos m + cos n )² = q²
cos² m + cos² n + 2 × cos m × cos n = q² ----(2)
On adding equation 1 and 2.
sin² m + sin² n + 2 × sin m × sin n + cos² m + cos² n + 2 × cos m × cos n = P² + q²
2 + 2 × sin m × sin n + 2 × cos m × cos n = P² + q²
sin m × sin n + cos m × cos n = \(\frac{P² + q² - 2 }{2}\)