(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Reduce the following series to the most simplified form:

1. 2 sin[tex]^{2}[/tex]([tex]\theta[/tex]/2)*(1+cos[tex]\theta[/tex])*(1+cos[tex]^{2}[/tex][tex]\theta[/tex])(1+cos[tex]^{4}[/tex][tex]\theta[/tex])............

2. tan ([tex]\theta[/tex]/2)*(1+sec [tex]\theta[/tex])(1+2[tex]\theta[/tex])(1+sec 4[tex]\theta[/tex])...................................

2. Relevant equations

For problem 1:

2 sin[tex]^{2}[/tex]([tex]\theta[/tex]/2)=1-cos[tex]\theta[/tex])

3. The attempt at a solution

For problem 1:

the result I got:

y=2[tex]^{(n+1)}[/tex]

Result=

1-cos[tex]^{y}[/tex][tex]\theta[/tex]

is it correct?????

For problem 2:

If I try to expand

sec 2 [tex]\theta[/tex]

I get huge denominators which are difficult to solve. Similarly with tan ([tex]\theta[/tex]/2),I again get a denominator with no pattern following any rule.

Please help me for the second one. and tell me if I am correct in solving the first problem.

regards,

Ritwik

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# Trigonometric Series

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