Question

(ii) Evaluate:
1-cos²A/2-sin²A, for A=60°

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Answer 1

Step-by-step explanation:

Given:-

1-cos^2 A/2-sin^2 A

To find:-

Evaluate 1-cos^2 A/2-sin^2 A, for A=60°

Solution:-

Method-1:-

Given that :

1-cos^2 A/2-sin^2 A

The value of 1-cos^2 A/2-sin^2 A ,if A = 60°

=>(1-cos^2 60°)/(2 -sin^2 60°)

=>[1-(1/2)^2]/[2-(√3/2)^2]

=>[1-(1/4)]/[2-(3/4)]

=>[(4-1)/4]/[(8-3)/4]

=>(3/4)/(5/4)

=>(3/4)×(4/5)

=>(3×4)/(4×5)

=>12/20

=>3/5

The value is 3/5

Method -2:-

Given that :

1-cos^2 A/2-sin^2 A

It cane be written as

(1-Cos^2 A) / (1+1-Sin^2 A)

=>(1-Cos^2 A)/(1+(1-Sin^2 A)

We know that Sin^2 A+ Cos^2 A = 1

=>Sin^2 A /(1+Cos^2 A)

If A = 60° then

=>Sin^2 60°/(1+Cos^2 60°)

=>(√3/2)^2 /[1+(1/2)^2]

=>(3/4)/[1+(1/4)]

=>(3/4)/(4+1)/4

=>(3/4)/(5/4)

=>(3/4)×(4/5)

=>3/5

The value = 3/5

Answer:-

The value of 1-cos^2 A/2-sin^2 A, for A=60° is 3/5

Used formulae:-

• Sin^2 A+ Cos^2 A = 1
• Sin 60° = √3/2
• Cos 60° = 1/2