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Prove that: (1+sec2theta)(1+sec4theta)(1...

Prove that: `(1+sec2theta)(1+sec4theta)(1+sec8theta)(1+sec2^ntheta)=t a n2^nthetacottheta, n in Ndot`

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Given,
`(1+sec2theta)(1+sec4theta)(1+sec8theta)...(1+sec2^ntheta)`
`⇒(1+1/(cos2theta))(1+sec4theta)(1+sec8theta)...(1+sec2^ntheta)`
`⇒(1+1/((1-tan^2theta)/(1+tan^2theta)))(1+sec4theta)(1+sec8theta)...(1+sec2^ntheta)`
`⇒(1+(1+tan^2theta)/(1-tan^2theta))(1+sec4theta)(1+sec8theta)...(1+sec2^ntheta)`
`⇒(1−tan^2(2theta))(1+sec4theta)(1+sec8theta)...(1+sec2^ntheta)`
Multiply with `tantheta` & also dividing the same.
`⇒1/(tantheta)((2tantheta)/(1−tan^2theta))(1+1/(cos^2(2theta)))(1+sec8theta)...(1+sec2^ntheta)`
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  3. Prove that: (1+sec2theta)(1+sec4theta)(1+sec8theta)(1+sec2^ntheta)=t a...

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  4. If theta=pi/(2^n+1) , prove that: 2^ncosthetacos2thetacos2^2 cos2^(n-1...

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  5. Prove that: cos(pi/7)cos((2pi)/7)cos((4pi)/7)=-1/8,

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  6. If alpha and beta are distict roots of acostheta+b sintheta=c , prov...

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  7. sin^2(A/2+pi/8) - sin^2(A/2-pi/8)= 1/sqrt(2)sinA

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  8. Sin 4A = 4 cos^3 A sin A - 4 sin^3 A cos A

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  9. If tanA=1/7a n dtanB=1/3 , show that cos2A=sin4Bdot

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  10. If 2t a nalpha/2=tan(beta/2) , prove that cosalpha=(3+5cosbeta)/(5+3c...

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  11. If acos2theta+bsin2theta=ch a salphaa n dbeta as its roots , then prov...

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  12. If cosalpha+cosbeta=0=sinalpha+sinbeta, then prove that cos2alpha+cos2...

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  13. Prove that: sin((pi)/5)sin((2pi)/5)sin((3pi)/5)sin((4pi)/5)=5/(16)

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  14. sin5theta =

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  15. Prove that: sin^4(pi/8)+sin^4((3pi)/8)+sin^4((5pi)/8)+sin^4((7pi)/8)=...

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  16. Prove that:tan6^0tan42^0tan66^0tan78^0=1.

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  17. If tanalpha=(1-cosbeta)/(sinbeta),t h e n a)tan3alpha=tan2beta (b...

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  18. Prove that: sin36^0=(sqrt(10-2sqrt(5)))/4 .

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  19. The value of (cos3theta)/(2cos2theta-1) is equal to costheta (b) sint...

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  20. The value of cos^4theta+sin^4theta-6cos^2theta is cos2theta (b) s in2...

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