Question

Let tan9° = `(1 - sqrt((sqrt(5)k)/m))k` where k = `sqrt(5) + 1` then m is equal to  ______.

Options

• 6.00

• 7.00

• 8.00

• 9.00

Answer 1

Let tan9° = `(1 - sqrt((sqrt(5)k)/m))k` where k = `sqrt(5) + 1` then m is equal to 8.00.

Explanation:

tan9° = `sin9^circ/cos9^circ`

= `(2sin^2 9^circ)/sin18^circ`

= `(1 - cos18^circ)/sin18^circ`

= `((1 - sqrt(10 + 2sqrt(5))/4))/(((sqrt(5) - 1))/4`

= `(1 - sqrt(10 + 2sqrt(5))/16)(sqrt(5) + 1)`

= `(1 - sqrt((sqrt(5)(sqrt(5) + 1))/8))(sqrt(5) + 1)`

⇒ m = 8