Related InterviewSolutions

• Prove that:`tan6^0tan42^0tan66^0tan78^0=1.`
• Prove that:`cos^4pi/8+cos^4(3pi)/8+cos^4(5pi)/8+cos^4(7pi)/8=3/2`
• Prove that: `(1+cospi/8)(1+cos(3pi)/8)(1+cos(5pi)/8)(1+cos(7pi)/8)=1/8`
• Prove that:`"cot"pi/(24)=sqrt(2)+sqrt(3)+sqrt(4)+sqrt(6)`
• Prove that `(tan3x)/(tanx)`never lies between `1/3a n d3`.
• Prove that:`sin(pi/10) sin((13pi)/10)=-1/4`
• Prove that `cos^3A+cos^3(120^0+A)+cos^3(240^0+A)=3/4cos3A`
• If `acos2theta+bsin2theta=ch a salphaa n dbeta`as its roots , then prove that`tanalpha+t a nbeta=(2a b)/(a+c)``tanalpha+t a nbeta=(c-a)/(c+a)``tan(alpha+beta)=b/a`
• Prove that: `|sintheta"sin"(60-theta)sin(60+theta)|lt=1/4`for all values of `theta`.
• If `theta=pi/(2^n+1)`, prove that: `2^ncosthetacos2thetacos2^2 cos2^(n-1)theta=1.`