Exemplar - Prove the following — task. Maths CBSE Live product, Class 10.

Prove that \((sin^4 \ \theta - cos^4 \ \theta + 1) cosec^2 \ \theta = 2\).

Proof:

{(\sin}^{4} θ - \cos^{4} θ + 1) {cosec}^{2} θ

By simplyfing this then we get,

By applying the identity

and simplyfing this then we get,

\(=\)

{(\sin}^{2} θ + \sin^{2} θ) {cosec}^{2} θ

\(= 2 \ sin^2 \ \theta \ cosec^2 \ \theta\)

\(= 2\)

Answer variants:

{[(\sin}^{2} θ - \cos^{2} θ) (1) + 1] {cosec}^{2} θ

{(\sin}^{2} θ + \sin^{2} θ) {cosec}^{2} θ

1 - \cos^{2} θ = \sin^{2} θ

{(\sin}^{4} θ - \cos^{4} θ + 1) {cosec}^{2} θ

Did you find an error?

2. Exemplar - Prove the following