sin A = cos A and tan²A + cot²A + 2 Statement (1): A = 45°, so tan²A + cot²A + 2 = 4 Statement (2): sin A = cos A ⇒ A = 45° 1. Both the statement are true. 2. Both the statement are false. 3. Statement 1 is true, and statement 2 is false. 4. Statement 1 is false, and statement 2 is true.

Given, sin A = cos A ⇒ = 1 ⇒ tan A = 1 ⇒ tan A = tan 45° ⇒ A = 45° So, statement 2 is true. Substituting value of A in tan2 A + cot2 A + 2, we get : ⇒ tan2 A + cot2 A + 2 = tan2 45° + cot2 45° + 2 = (1)2 + (1)2 + 2 = 1 + 1 + 2 = 4. So, statement 1 is true. ∴ Both the statements are true. Hence, option 1 is the correct option.

Mathematics

sin A = cos A and tan² A + cot² A + 2
Statement (1): A = 45°
tan² A + cot² A + 2 = 4
Statement (2): sin A = cos A ⇒ A = 45°
Both the statement are true.
Both the statement are false.
Statement 1 is true, and statement 2 is false.
Statement 1 is false, and statement 2 is true.

Trigonometric Identities

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Answer

Given, sin A = cos A

⇒ $\dfrac{\text{sin A}}{\text{cos A}}$ = 1

⇒ tan A = 1

⇒ tan A = tan 45°

⇒ A = 45°

So, statement 2 is true.

Substituting value of A in tan² A + cot² A + 2, we get :

⇒ tan² A + cot² A + 2 = tan² 45° + cot² 45° + 2

= (1)² + (1)² + 2

= 1 + 1 + 2

= 4.

So, statement 1 is true.

∴ Both the statements are true.

Hence, option 1 is the correct option.

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Mathematics

sin A = cos A and tan² A + cot² A + 2
Statement (1): A = 45°
tan² A + cot² A + 2 = 4
Statement (2): sin A = cos A ⇒ A = 45°
Both the statement are true.
Both the statement are false.
Statement 1 is true, and statement 2 is false.
Statement 1 is false, and statement 2 is true.

Trigonometric Identities

Answer

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$1 - \dfrac{\text{sin}^2 A}{\text{1 + cos A}} = \text{cos A}$

Mathematics

sin A = cos A and tan2 A + cot2 A + 2Statement (1): A = 45°tan2 A + cot2 A + 2 = 4Statement (2): sin A = cos A ⇒ A = 45°Both the statement are true.Both the statement are false.Statement 1 is true, and statement 2 is false.Statement 1 is false, and statement 2 is true.

Trigonometric Identities

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sin A = cos A and tan² A + cot² A + 2
Statement (1): A = 45°
tan² A + cot² A + 2 = 4
Statement (2): sin A = cos A ⇒ A = 45°
Both the statement are true.
Both the statement are false.
Statement 1 is true, and statement 2 is false.
Statement 1 is false, and statement 2 is true.

Prove the following identities :
$\dfrac{1}{\text{cos A + sin A}} + \dfrac{1}{\text{cos A - sin A}} = \dfrac{\text{2 cos A}}{\text{2 cos}^2 A - 1}$

Prove the following identities :
$1 - \dfrac{\text{sin}^2 A}{\text{1 + cos A}} = \text{cos A}$