Question

sec² = 1 + tan² Q , sec ² = 1_ ( 7/24)²​

Answer 1

Answer:

Solution :

1) To prove : “ sin² θ + 1 / (1+ tan² θ ) = 1 ”

2) Inference ( Understanding the question, Thinking of the method ) : We shall start from Left hand side ( L. H. S) and proceed till we get R. H. S. We will use trigonometric identities too.

3) Formulas we are going to use :

arrowarrow 1/secθ = cosθ

arrowarrow tan²θ +1 = sec²θ

arrowarrow sin²θ + cos²θ = 1

4) Actual proof :

Firstly, We know that, tan²θ +1 = sec²θ

\begin{gathered}\\ \implies Left \: hand \: side \: \\ \implies sin^2 \theta + \frac {1}{1 + tan^2 \theta} \\ \implies (sin^2 \theta) + \frac{1}{sec^2 \theta} \\ \implies ( sin^2 \theta) + (cos^2 \theta) \\ \implies 1 \\ \implies Right \: Hand \: side\end{gathered}

⟹Lefthandside

⟹sin

2

θ+

1+tan

2

θ

1

⟹(sin

2

θ)+

sec

2

θ

1

⟹(sin

2

θ)+(cos

2

θ)

⟹1

⟹RightHandside

Therefore, We proved the identity sin² θ + 1 / (1+ tan² θ ) = 1

Hope it helps!