Exact Form:
√2−1
Decimal Form:
0.41421356
…
Step-by-step explanation:
Since  9π/8  is not an angle where the values of the six trigonometric functions are known, try using half-angle identities.
9Ï€/8 Â is not an exact angle
First, rewrite the angle as the product of  1/2  and an angle where the values of the six trigonometric functions are known. In this case,  9π/8  can be rewritten as
(1/2)* Â 9Ï€/8 tan ((1/2)* Â 9Ï€/8)
Use the half-angle identity for tangent to simplify the expression. The formula states that Â
tan (0/2)=sin(0)/1+cos(0) sin(9Ï€/4)/1+cos(9Ï€/4)
Simplify
Remove full rotations of  2π  until the angle is between  0  and  2π.
sin(Ï€/4)/1+cos(9Ï€/4)
The exact value of sin(π/4) is √2/2
√2/2/1+cos(9π/4)
Simplify the Denominator
Remove full rotations of  2π  until the angle is between  0  and  2π.√2/2/1+cos(π4)
The exact value of cos(π/4)  is  √2/2.√2/2/1+√2/2
To write  1/1  as a fraction with a common denominator, multiply by  2/2  .√2/2/1/1⋅2/2+√2/2
Write each expression with a common denominator of  2, by multiplying each by an appropriate factor of  1.
Combine.
√2/2/1⋅2/1⋅2+√2/2
Multiply 2 by 1
√2/2/1⋅2/2+√2/2
Combine the numerators over the common denominator.
√2/2/1⋅2+√2/2
Multiply 2 by 1
√2/2/2+√2/2
Multiply the numerator by the reciprocal of the denominator
√2/2  ⋅  2/2+√2
Cancel the common factor of  2  .
Factor out the greatest common factor  2
√2/2⋅1  ⋅  2⋅1/2+√2
Cancel the common factor
√2/2⋅1  ⋅  2⋅1/2+√2
Rewrite the expression.
√2/1  ⋅  1/2+√2
Simplify
Multiply  √2/1  and  1/2+√2
√2/2+√2
Multiply  √2/2+√2  by  2−√2/2−√2
Combine
√2(2−√2)/(2+√2)(2−√2)
Expand the denominator using the FOIL method.
√2(2−√2)/4−2√2+√2⋅2−√2^2
Simplify
√2(2−√2)/2
Apply the distributive property
√2⋅2+√2(−√2)/2
Move  2  to the left of the expression  √2⋅2.
2⋅√2+√2(−√2)/2
Simplify Â
√2(−√2)  .
Raise  √2  to the power of  1  .
2⋅√2−(√2^1√2)/2
Raise  √2  to the power of  1  .
2⋅√2−(√2^1√2^1)/2
Use the power rule  a^m  a^n=a^m+n  to combine exponents.
2⋅√2−√2^1+1/2
Add  1  and  1  .
2⋅√2−√2^2/2
Simplify each term.
Multiply  2  by  √2  .
2√2−√2^2/2
Rewrite  √2^2  as  2  .
2√2−1⋅2/2
Multiply  −1  by  2.
2√2−2/2
Reduce the expression by cancelling the common factors.
Factor  2  out of  2√2.
2(√2)−2/2
Factor  2  out of  −2.
2(√2)+2⋅−1/2
Factor  2  out of Â
2(√2)+2(−1)2(√2−1)/2
Cancel the common factors.
Factor  2  out of  2  .
2(√2−1)/2(1)
Cancel the common factor.
2(√2−1)/2⋅1
Rewrite the expression.
√2−1/1
Divide  √2−1  by  1  .
√2−1
The result can be shown in multiple forms.
Exact Form:
√2−1
Decimal Form:
0.41421356…
Hope it help. Good luck.
