Question

Simplify:

Class 10

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Answer 1

Answer:

The answer for the above given simplification is 1.

Step-by-step explanation:

Given Equation: [(sin³θ+cos³θ)/(sinθ + cosθ)] + (sinθcosθ)

Lets break down the above equation into simple steps to get the answer.

Applying the Algebraic formula , a³ + b³ = (a + b)(a² - ab + b²)

= [{(sinθ+cosθ)(sin²-sinθcosθ+cos²θ)}/(sinθ + cosθ)] + (sinθcosθ)

= sin²θ - sinθcosθ + cos²θ + sinθcosθ …. [cancelling (sinθ+cosθ) from numerator and denominator]

= sin²θ + cos²θ

= 1 ….. [ Trignometric identity : sin²θ + cos²θ = 1]

Answer 2

Answer:

(Sin³θ + Cos³θ )/(sinθ + Cosθ)   + SinθCosθ = 1

Step-by-step explanation:

(Sin³θ + Cos³θ )/(sinθ + Cosθ)   + SinθCosθ

= (Sin³θ + Cos³θ )/(sinθ + Cosθ)  + SinθCosθ(sinθ + Cosθ)/(sinθ + Cosθ)

= (Sin³θ  + Sin²θCosθ+ Cos³θ  + SinθCos²θ)/(sinθ + Cosθ)

= (Sin³θ + Sin²θCosθ + Cos³θ  + SinθCos²θ)/(sinθ + Cosθ)

=  (Sin²θ(Sinθ + Cosθ) + Cos²θ(Cosθ  + Sinθ)/(sinθ + Cosθ)

=  (Sin²θ(Sinθ + Cosθ) + Cos²θ(Sinθ + Cosθ)/(sinθ + Cosθ)

= (Sin²θ + Cos²θ)(Sinθ + Cosθ)/(sinθ + Cosθ)

= (Sin²θ + Cos²θ)

= 1

(Sin³θ + Cos³θ )/(sinθ + Cosθ)   + SinθCosθ = 1