Q) If = p and = q, then prove that (p ²– q ²) sec ² α = p ²

(Q 26 B – 30/2/2 – CBSE 2026 Question Paper)

Ans: 

Step 1: Given that:

= p   and   = q

With the help of given values, first let’s develop the given equation to prove:

(p ²– q ²) sec ² α = p ²

∴ . sec ² α =

Step 2: Let’s start from LHS:

. sec ² α

= . sec ² α

= . sec ² α

Step 3: Since 1 + tan ² θ  = sec ² θ

∴ sec ² θ  – tan ² θ  = 1

and ∴ sec ² α  – tan ² α  = 1

Step 4: By substituting this value in LHS, we get:

LHS = . sec ² α

= . sec ² α

=

=  = RHS

Hence Proved!

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