Question

How to do this question by proving the identity?

Answer 1

• Refer the attachment

Additional Information :

• ⇒ sin² θ + cos² θ = 1
• ⇒ sin² θ = 1 - cos²θ
• ⇒ sec²θ = 1 + tan²θ
• ⇒ cot²θ = cosec²θ - 1

★ Reciprocal identities :-

`\boxed{sin θ = (1)/(cosecθ)}`

`\boxed{cosec θ = (1)/( sin θ)}`

`\boxed{cos θ = (1)/( sec θ)}`

`\boxed{sec θ = (1)/(cos θ)}`

`\boxed{tan θ = (1)/( cot θ)}`

`\boxed{cot θ = (1)/(tan θ)}`

Answer 2

`\sin^3 \theta-\cos^3 \theta=(\sin \theta-\cos \theta)(\sin \theta\cos \theta+1)\\\\ (\sin \theta-\cos \theta)(\sin^2 \theta+\sin \theta\cos \theta +\cos^2 \theta)=(\sin \theta-\cos \theta)(\sin \theta\cos \theta+1)\\\\ (\sin \theta-\cos \theta)(\sin \theta\cos \theta+1)=(\sin \theta-\cos \theta)(\sin \theta\cos \theta+1)\\\\`