Solve the following to find its value in terms of trigonometric ratios.
(sin A + cos A)(1 – sin A cos A)
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. sin3 A + cos3 A.
Sin2A + cos2A = 1 ---- (1)
a3 + b3 = (a + b)(a2 + b2 - ab) ---- (2)
⇒ (sin A + cos A)(1 – sin A cosA)
Using equation (1)
⇒ (sin A + cos A)(sin2A+ cos2A – sin A cosA)
Using equation (2), we get
⇒ sin3A + cos3A