Trigonometry class 10!

1.	Trigonometry class 10!
Answer» Answer: 17/5 Step-by-step explanation: given:- COTA = 12/15 As we know, By the FORMULA, cosec²A - cot²A = 1 => cosec²A = 1+cot²A => cosec²A = 1+(12/15)² => cosec²A = 1+144/225 = (25+144)/25 = 169/25 => cosec A = √(169/25) = 13/5 Also, sinA = 1/COSECA = 1÷(13/5) = 5/13 Now, by the formula, sin²A + cos²A = 1 => cos²A = 1-sin²A => cos²A = 1-(5/13)² = 1-25/169 => cos²A = (169-25)/169 = 144/164 => COS A = √(144/169) = 12/13 ATQ, (sinA + cosA) × cosecA = (5/13 + 12/13) × 13/5 (sinA + cosA) × cosecA = 17/13 × 13/5 = 17/5

Answer»

Answer:

17/5

Step-by-step explanation:

given:-

COTA = 12/15

As we know,

By the FORMULA,

cosec²A - cot²A = 1

=> cosec²A = 1+cot²A

=> cosec²A = 1+(12/15)²

=> cosec²A = 1+144/225 = (25+144)/25 = 169/25

=> cosec A = √(169/25) = 13/5

Also,

sinA = 1/COSECA = 1÷(13/5) = 5/13

Now, by the formula,

sin²A + cos²A = 1

=> cos²A = 1-sin²A

=> cos²A = 1-(5/13)² = 1-25/169

=> cos²A = (169-25)/169 = 144/164

=> COS A = √(144/169) = 12/13

ATQ,

(sinA + cosA) × cosecA = (5/13 + 12/13) × 13/5

(sinA + cosA) × cosecA = 17/13 × 13/5 = 17/5

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