prove that (1+cos a+cosec)(1+tan a+sec a)=2
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Here it will be cotA not cosA
To Prove: (1 + cotA - cosecA)(1 + tanA + secA) = 2
Remember before;
- cosecA = 1/sinA
- secA = 1/cosA
- tanA = sinA/cosA
- cotA = cosA/sinA
→ (1 + cosA/sinA - 1/sinA)(1 + sinA/cosA + 1/cosA)
→ (sinA + cosA - 1)/sinA × (cosA + sinA + 1)/cosA
→ [(sinA + cosA)² - 1²]/sinA cosA
→ [sin²A + cos²A + 2sinA cosA - 1]/sinA cosA
→ (1 + 2sinA cosA - 1)/sinA cosA
→ 2 sinA cosA/sinA cosA
→ 2
Hence Proved
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