Question

Prove sin²A +cos²A=1 , sec²A=1+tan²A and cosec²A=1+cot²A. prove with taking an diagram as example as proof.

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Answer 1

Answer:

Sin²A.cot²A+cos²A.tan²A =Sin²A.cos²A/sin²A +cos²A.sin²A/cos²A =Cos²A+Sin²A =1 Proved

Answer 2

Answer:

1. sin²A + cos²A = 1

value of sin is p/h

value of cos is b/h

• LHS
• sin²A + cos²A
• (p/h)² + (b/h)²
• p²/h² + b²/h²
• (p²+b²)/h²
• h²/h²
• 1. RHS

2. 1 + tan²A = sec²

we know that tan is p/b

sec is h/b

• LHS,
• 1 + tan²A
• 1 + (p/b)²
• 1 + p²/b²
• (b² + p²) / b²
• h²/b²
• sec²A RHS

3. 1 + cot²A = cosec²A

we know that cot is b/p

cosec is h/p

• LHS,
• 1 + cot²A
• 1 + (b/p)²
• 1 + b²/p²
• (p² + b²) / p²
• h²/p²
• cosec²A RHS

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