Question

Sincubetheta+coscube theta /Sintheta +costheta

Answer 1

Step-by-step explanation:

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Answer 2

we know that:- (x³ + y³) = (x + y)(x² + y² - xy)

and (sin²Ф + cos²Ф) = 1

Now the given questions is:- \bold{\frac{sin^3\theta + cos^3\theta}{sin\theta + cos\theta} + sin\theta*cos\theta}

now, using the formula of (x³ + y³) in the place of (sin³Ф + cos³Ф).

\bold{\frac{(sin\theta + cos\theta)(sin^2\theta + cos^2\theta - sin\theta*cos\theta)}{sin\theta + cos\theta} + sin\theta * cos\theta}

\bold{[(sin^2\theta + cos^2\theta) - sin\theta * cos\theta] + sin\theta * cos\theta}

\bold{1 - sin\theta * cos\theta + sin\theta * cos\theta}

\bold{=1}

\boxed{\large{\bold{HENCE, \frac{sin^3\theta + cos^3\theta}{sin\theta + cos\theta} + sin\theta*cos\theta = 1