Home
Class 12
MATHS
Prove that: "tan"pi/(16)=sqrt(4+2sqrt(2)...

Prove that: `"tan"pi/(16)=sqrt(4+2sqrt(2))-(sqrt(2)+1)`

Text Solution

Verified by Experts

`tan ""(pi)/(16)=tan 11.25^(@)`
We know that on `22.5^(@)=sqrt(2)-1`
`tan 2theta=(2tan theta)/(1-tan^(2)theta)`
Put `theta=11.5^(@)`
`therefore tan 22.5^(@)=(2 tan 11.25^(@))/(1-tan^(2)11.25^(@))`
`therefore (sqrt(2)-1)x^(2)+2x-(sqrt(2)-1)=0`, where `x=tan 11.25^(@)`
`therefore x=(-2+sqrt(4+4(sqrt(2)-1))^(2))/(2(sqrt(2)-1))`
`(-1)/(sqrt(2)-1)+(sqrt(4-2sqrt(2)))/(sqrt(2)-1)`
`=-(sqrt(2)+1)+sqrt(4-2sqrt(2)).(sqrt(2)+1)`
`=-(sqrt(2)+1)+sqrt((4-2sqrt(2))(sqrt(2)+1)^(2))`
`=-(sqrt(2)+1)+sqrt((4-2sqrt(2))(3+2sqrt(2)))`
`=-(sqrt(2)+1)+sqrt(4+2sqrt(2))`
Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRIC RATIOS AND TRANSFORMATION FORMULAS

    CENGAGE ENGLISH|Exercise Solved example|15 Videos

  • TRIGONOMETRIC RATIOS AND TRANSFORMATION FORMULAS

    CENGAGE ENGLISH|Exercise Concept App. 3.1|11 Videos

  • TRIGONOMETRIC FUNCTIONS

    CENGAGE ENGLISH|Exercise SINGLE CORRECT ANSWER TYPE|38 Videos

  • TRIGONOMETRIC RATIOS FOR COMPOUND, MULTIPLE, SUB-MULTIPLE ANGLES, AND TRANSFORMATION FORMULAS

    CENGAGE ENGLISH|Exercise Multiple Correct Answers Type|6 Videos

Similar Questions

Explore conceptually related problems

Prove that tanpi/(16)=sqrt(4+2sqrt(2))-(sqrt(2)+1)

Prove that: "tan"142""(1^0)/2=2+sqrt(2)-sqrt(3)-sqrt(6)

Prove that: "cot"pi/(24)=sqrt(2)+sqrt(3)+sqrt(4)+sqrt(6)

Prove that tan^(-1)[(sqrt(1+x^2)+sqrt(1-x^2))/(sqrt(1+x^2)-sqrt(1-x^2))]=pi/4+1/2cos^(-1)x^2

Prove that: tan^(-1){(sqrt(1+x)-sqrt(1-x))/(sqrt(1+x)+sqrt(1-x))}=pi/4-1/2. cos^(-1)x , 0

Prove that: tan^(-1) {(sqrt(1+x)-sqrt(1-x))/(sqrt(1+x)+sqrt(1-x))} = pi/4-1/2\ cos^(-1)x

Prove that: tan^(-1)[(sqrt(1+x)-sqrt(1-x))/(sqrt(1+x)+sqrt(1-x))]=pi/4-1/2cos^(-1)x ,\ -1/(sqrt(2))\ lt=x\ lt=1

Prove that tan^(-1)((sqrt(1+x)-sqrt(1-x))/(sqrt(1+x)+sqrt(1-x)))=pi/4-1/2cos^(-1)x,-1/(sqrt(2))lt=xlt=1

Prove that tan^(-1)((sqrt(1+x)-sqrt(1-x))/(sqrt(1+x)-sqrt(1-x)))=pi/4-1/2cos^(-1),-1/(sqrt(2))lt=xlt=1

Prove that tan [7(1)/(2)]^0 = (sqrt(3) - sqrt(2)) (sqrt(2) - 1) .