Question

cos^2 π/4+sin^2(3π/4)+sin^2(5π/4)+sin^2(7π/4)=2 proof

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Answer 1

Answer:

sin

2

(2π/3)+cos

2

(5π/6)−tan

2

(3π/4)

=sin

2

(π−π/3)+cos

2

(π−π/6)−tan

2

(π−π/4)

=(sin(π/3))

2

+(−cos(π/6))

2

−(−tanπ/4)

2

⎣

⎢

⎢

⎡

sin(π−x)=sinx

cos(n−x)=−cosx

tan(π−x)=−tanx

⎦

⎥

⎥

⎤

=(

2

3

)

2

+(

2

−

3

)

2

−(−1)

2

=

4

3

+

4

3

−1

=

4

6

−1

=

4

2

=

2

1

∴sin

2

(2π/3)+cos

2

(5π/6)−tan

2

(3π/4)=1/2.

Answer 2

Answer:

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