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Q) Prove that: (1 + cot θ – cosec θ) (1 + tan θ + sec θ) = 2.
(Q 31 – 30/5/2 – CBSE 2026 Question Paper)
Ans:
Step 1: Let’s start from LHS:
LHS = (1 + cot θ – cosec θ) (1 + tan θ + sec θ)
= 
= 
= 
Step 2: By algebraic identity, (a – b) (a + b) = a 2 – b 2
∴ LHS = 
= 
Step 3: By algebraic identity, (a + b) 2 = a 2 + b 2 + 2 ab
∴ LHS = 
Step 4: ∵ By trigonometric identity, sin 2 θ + cos 2 θ = 1
∴ LHS = 
= 
= 
= 
= 2 = RHS
Hence Proved !
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