Question

If sintita =3/5 and costita=4/5.find the values sinsquaretita+cossquaretita.

Answer 1

Answer

The required value is 1

Given

$\bullet \: \: \rm \sin \theta = \dfrac{3}{5} \: \: \: and \: \: \: \cos \theta = \dfrac{4}{5}$

To Find

$\bullet \: \: \rm \sin {}^{2} \theta + \cos{}^{2} \theta$

Solution

Given ,

$\sf \sin \theta = \dfrac{3}{5} \\ \\ \sf\implies {( \sin \theta)}^{2} = ({ \frac{3}{5}})^{2} \\ \\ \sf\implies { \sin}^{2} \theta = \frac{9}{25} \: - - \longrightarrow(1)$

Again ,

$\sf\cos \theta = \dfrac{4}{5} \\ \\ \sf \implies ({ \cos \theta)}^{2} = (\frac{4}{5} ) {}^{2} \\ \\ \sf \implies { \cos }^{2} \theta = \frac{16}{25} \: - - \longrightarrow(2)$

Adding (1) and (2) we have :

$\sf \sin^{2} \theta + { \cos }^{2} \theta = \dfrac{9}{25} + \dfrac{16}{25} \\ \\ \sf \implies \sin^{2} \theta + { \cos }^{2} \theta = \frac{9 + 16}{25} \\ \\ \sf \implies \sin^{2} \theta + { \cos }^{2} \theta = \frac{25}{25} \\ \\ \sf \implies \sin^{2} \theta + { \cos }^{2} \theta =1$

Answer 2

Given ,

sinθ = 3/5

cosθ = 4/5

$\implies \bold{sin^2\theta+cos^2\theta}\\\\\implies \bold{(\frac{3}{5} )^2+(\frac{4}{5})^2}\\\\\implies \bold{\frac{9}{25} +\frac{16}{25} }\\\\\implies \bold{\frac{25}{25} }\\\\\implies \bold{1}$

$\bold{So}\;\;\; \underline{\bold{\bf{\blue{ sin^2\theta+cos^2\theta=1}}}}$

More Information :

$\underbrace{\bold{\bf{\red{Trigonometric\ Identities :}}}}$

• sin²θ + cos²θ = 1
• sec²θ - tan²θ = 1
• cosec²θ - cot²θ = 1