Question

sin^2 ∅ + 1/1+tan^2∅​

Answer 1

Answer:

1

Step-by-step explanation:

${ \sin }^{2} + \frac{1}{1 + { \tan }^{2} }$

${ \sin }^{2} + \frac{1}{ { \sec}^{2}} \: \: \: \: \: \: \: \: \: \: \: ({ \tan}^{2} + 1 = { \sec }^{2})$

${ \sin }^{2} + { \cos}^{2} = 1 \: \: \: \: \: \: ( { \cos}^{2} = \frac{1}{ { \sec }^{2} } )$

$= 1$

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Answer 2

$\Large{\bf{\green{\mathfrak{\dag{\underline{\underline{Given:-}}}}}}}$

• $\sf sin^2 A \: + \: \dfrac{1}{1 \: + \: tan^2 A}$

$\Large{\bf{\red{\mathfrak{\dag{\underline{\underline{Solution:-}}}}}}}$

• $\sf sin^2 A \: + \: \dfrac{1}{1 \: + \: tan^2 A}$

We know that,

• 1 + tan² A = sec² A

Substituting the values,

• $\sf sin^2 A \: + \: \dfrac{1}{sec^2 A}$

• $\sf sin^2 A \: + \: \Big(\dfrac{1}{sec \: A}\Big)^2$

We know that,

• 1 / sec A = cos A

Substituting the values,

• sin² A + (cos A)²

• sin² A + cos² A

We know that,

• sin² A + cos² A = 1

Therefore,

• $\boxed{\purple{\sf sin^2 A \: + \: \dfrac{1}{1 \: + \: tan^2 A} \: = \: 1}}$