Question

the absolute value of the expression tan π/16 +tan5π/16+tan 9π/16+13π/16 is​

Answer 1

Answer:

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Answer 2

Step-by-step explanation:

tan

16

π

+tan

16

5π

+tan

16

9π

+tan

16

13π

⟹

cos

16

π

sin

16

π

+

cos

16

9π

sin

16

9π

+

cos

16

5π

sin

16

5π

+

cos

16

13π

sin

16

13π

weknowthatsin(A+B)=sinAcosB+cosAsinB

And2cosAcosB=cos(A+B)+cos(A−B)

Soweget

⟹

cos

16

π

cos

16

9π

sin

16

π

cos

16

9π

+sin

16

9π

cos

16

π

+

cos

16

5π

cos

16

13π

sin

16

5π

cos

16

13π

+sin

16

13π

cos

16

5π

⟹

cos

16

10π

+cos

2

π

2sin

16

10π

+

cos

16

18π

+cos

2

π

2sin

16

18π

⟹

cos

8

5π

2sin

8

5π

+

cos

8

9π

2sin

8

9π

⟹

cos

8

5π

cos

8

9π

2sin

8

14π

⟹

cos

4

7π

+cos

2

π

4sin

4

7π

⟹4tan

4

7π

=−4

Sotheabsolutevalueis4