Question

Period of tan theta(1+sec2theta)(1+sec4thta)(1+sec8theta) is π /β then β =

Answer 1

Answer:

Step-by-step explanation:

hi

ur answer is in the attachment below, hope it helps

pls mark me as brainliest

Answer 2

Given :   Period of tan theta(1+sec2theta)(1+sec4thta)(1+sec8theta) is π /β  

To find : β

Solution:

Tanθ (1  + Sec2θ) (1 + Sec4θ)(1 + Sec8θ)

= (Sinθ/Cosθ)(1  + 1/Cos2θ)(1 + 1/Cos4θ)(1 + 1/Cos8θ)

=  (Sinθ/Cosθ)((1  + Cos2θ)/Cos2θ)((1 + Cos4θ)/Cos4θ)((1 + Cos8θ)/Cos8θ)

Using 1  + Cos2θ = 2Cos²θ

=  (Sinθ/Cosθ)( 2Cos²θ)/Cos2θ)((1 + Cos4θ)/Cos4θ)((1 + Cos8θ)/Cos8θ)

= (2SinθCosθ / Cos2θ) ((1 + Cos4θ)/Cos4θ)((1 + Cos8θ)/Cos8θ)

Using  Sin2θ = 2SinθCosθ

= (Sin2θ / Cos2θ) ((1 + Cos4θ)/Cos4θ)((1 + Cos8θ)/Cos8θ)

= (Sin2θ / Cos2θ) ((2Cos²2θ)/Cos4θ)((1 + Cos8θ)/Cos8θ)

= (2Sin2θCos2θ /Cos4θ)((1 + Cos8θ)/Cos8θ)  

=  ( Sin4θ/Cos4θ)((1 + Cos8θ)/Cos8θ)  

=( Sin4θ/Cos4θ)((2Cos²4θ)/Cos8θ)  

= ( 2Sin4θ Cos4θ)/Cos8θ

= Sin8θ/Cos8θ

= Tan8θ  

Period of Tanθ  is  π

=> 8θ  = π

=> θ  = π/8

π/8  = π /β

=> β = 8

Learn more:

find the period of f(x)=sinx+sin^2x+sin^3x+.....................+sin^2020x ...

https://brainly.in/question/17354656

Find the period of the function: tan (x + 4x +9x + ... + n²x) (n is any ...

brainly.in/question/6963869

Find the period of the function cos(4x+9/5) - Brainly.in

brainly.in/question/8408354