Question

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Plss help me
Solve any two​

Answer 1

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Question :-

• Prove the following trigonometric identities
• (i)
• $(i)(1 - { \sin }^{2}Ѳ) { \sin}^{2}Ѳ = 1 \\ \\( ii) { \cos }^{2} Ѳ(1 + { \tan}^{2} Ѳ) = 1$

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Answer:-

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Step by step explanation:-

(i)(1 - { \sin }^{2}Ѳ) { \sin}^{2}Ѳ = 1

Ans :-

We have ,

First see LHS side

$⇒(1 - { \sin}^{2}Ѳ) { \sec }^{2} Ѳ \\ \\ ⇒ { \cos }^{2} Ѳ { \sin }^{2} Ѳ \\ \\ ⇒ { \cos }^{2} Ѳ (\frac{1}{ { \cos }^{2}Ѳ } ) \\ \\ ⇒1$

So LHS = RHS

(ii) Cos ^2 Ѳ(1+tan^2 Ѳ) = 1

Ans:-

Take LHS side

$⇒ { \cos }^{2} Ѳ(1 + { \tan }^{2} Ѳ) \\ \\ ⇒ { \cos }^{2} Ѳ { \sec }^{2}Ѳ \\ \\ ⇒ { \cos }^{2} Ѳ ( \frac{1}{ { \cos}^{2} }Ѳ ) \\ \\ ⇒1$

So LHS = RHS

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