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SVEN [57.7K]
2 years ago
7

Verify that (cos²a) (2 + tan² a) = 2 - sin² a....​

Mathematics
2 answers:
Sveta_85 [38]2 years ago
7 0

Trigonometric Formula's:

\boxed{\sf \ \sf \sin^2 \theta + \cos^2 \theta = 1}

\boxed{ \sf tan\theta = \frac{sin\theta}{cos\theta} }

Given to verify the following:

\bf (cos^2a) (2 + tan^2 a) = 2 - sin^2 a

\texttt{\underline{rewrite the equation}:}

\rightarrow \sf (cos^2a) (2 + \dfrac{sin^2 a}{cos^2 a} )

\texttt{\underline{apply distributive method}:}

\rightarrow \sf 2 (cos^2a) + (\dfrac{sin^2 a}{cos^2 a} ) (cos^2a)

\texttt{\underline{simplify the following}:}

\rightarrow \sf 2cos^2 a  + sin^2 a

\texttt{\underline{rewrite the equation}:}

\rightarrow \sf 2(1 - sin^2a )  + sin^2 a

\texttt{\underline{distribute inside the parenthesis}:}

\rightarrow \sf 2 - 2sin^2a   + sin^2 a

\texttt{\underline{simplify the following}} :

\rightarrow \sf 2 - sin^2a

Hence, verified the trigonometric identity.

Artemon [7]2 years ago
7 0

Answer:

See below ~

Step-by-step explanation:

Identities used :

⇒ cos²a = 1 - sin²a

⇒ tan²a = sin²a / cos²a

============================================================

Solving :

⇒ (cos²a) (2 + tan² a)

⇒ 2cos²a + (cos²a)(tan²a)

⇒ 2(1 - sin²a) + sin²a

⇒ 2 - 2sin²a + sin²a

⇒ 2 - sin²a [∴ Proved √]

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