Q58 of 58 Page 77

State True or False for the statements

The maximum value of is 1/2.

True

Given


Performing operations R2→ R2 – R1 and R3→ R3 – R1



= cos θ. sin θ


Multiply and divide by 2,


= 1/2 (2sin θ cos θ)


We know that 2 sin θ cos θ = sin 2θ


= 1/2 (sin 2θ)


Since the maximum value of sin 2θ is 1, θ = 45°.


∴ Δ = 1/2 (sin 2(45°))


= 1/2 sin 90°


= 1/2 (1)


∴ Δ = 1/2


Hence the above statement is true.


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