Question

How to do this question by proving the identity?

Answer 1

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

Answer 2

Solution :

• Refer the attachment

Additional Information :

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

★ Reciprocal identities :-

$\boxed{sin θ = \dfrac{1}{cosecθ}}$

$\boxed{cosec θ = \dfrac{1}{ sin θ}}$

$\boxed{cos θ = \dfrac{1}{ sec θ}}$

$\boxed{sec θ = \dfrac{1}{cos θ}}$

$\boxed{tan θ = \dfrac{1}{ cot θ}}$

$\boxed{cot θ = \dfrac{1}{tan θ}}$