Question

What is the value of $sin^{2}\Theta+\frac{1}{1+tan^{2}\Theta }$?

Answer 1

Answer:

The value of sin²θ + 1/(1+ tan²θ) is  1 .

Step-by-step explanation:

Given : sin²θ + 1/(1+ tan²θ)

= sin²θ + 1/sec²θ

[By using the identity ,1 + tan²θ = sec²θ]

= sin²θ + (1/secθ)²

= sin²θ + cos²θ

[By using the identity ,1 /secθ = cosθ]

= 1

[By using the identity , sin² θ + cos² θ = 1]

Hence , the value of sin²θ + 1/(1+ tan²θ) is  1 .

HOPE THIS ANSWER WILL HELP YOU…

Answer 2

Answer:

▶Here's your answer

⏩Let theta be x...

${ \sin(x) }^{2} + \frac{1}{1 + { \tan(x) }^{2} }$

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

▶Since sec (theta ) =1/cos (theta)

⏩The answer is 1...

Hope it helps ✌