(secA+tanA)(1-sinA)=? | 10th,11th,CBSE,ICSE,JEE,STATE BOARD

(secA+tanA)(1-sinA)=? | 10th,11th,CBSE,ICSE,JEE,STATE BOARD

1. "Trigonometry | (secA+tanA)(1-sinA) = ? | 10th, 11th, CBSE, ICSE"
2. "Solve: (secA+tanA)(1-sinA) | Trigonometric Identities | JEE, State Board"
3. "Trigonometry Proof | (secA+tanA)(1-sinA) = 1 | 10th, 11th Maths"

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"Solve the trigonometric expression: (secA+tanA)(1-sinA).

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Solution:

(secA+tanA)(1-sinA)

= (1/cosA + sinA/cosA)(1-sinA)

= (1 + sinA)/cosA(1-sinA)

= (1 - sin²A)/cosA(1-sinA)

Using Pythagorean identity: 1 - sin²A = cos²A

= cos²A/cosA(1-sinA)

= cosA/(1-sinA)

= 1/(1-sinA) × cosA

= 1

Hence, (secA+tanA)(1-sinA) = 1.