split up if u can [2]

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tan(x/2)sec(x)+tan(x/2^{2})sec(x/2)+tan(x/2^{3})sec(x/^{2})+...........................+tan(x/2^{n})sec(x/2^{n-1})

cotx-cot(x/2^{n}) cotx-tan(x/2^{n}) tanx-cot(x/2^{n}) tanx-tan(x/2^{n})

Atul Solanki by Atul Solanki , 23, India

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1 solution

U Z
Nov 6, 2014

t a n x 2 s e c x = s i n x 2 c o s x 2 c o s x = s i n ( x − x 2 c o s x 2 c o s x tan\frac{x}{2}secx = \frac{sin{x}{2}}{cos\frac{x}{2}cosx} = \frac{sin( x - \frac{x}{2}}{cos\frac{x}{2}cosx}

= s i n x c o s x 2 − c o s x c o s x 2 c o s x 2 c o s x = \frac{sinxcos\frac{x}{2} - cosxcos\frac{x}{2}}{cos\frac{x}{2}cosx}

similarly 2nd term and so on ....

t a n x − t a n x 2 + t a n x 2 − t a n x 2 2 + t a n x 2 2 + . . . . . t a n x 2 n − 1 − t a n x 2 n tanx - tan\frac{x}{2} + tan\frac{x}{2} - tan\frac{x}{2^{2}} +tan\frac{x}{2^{2}} + ..... tan\frac{x}{2^{n-1}} - tan\frac{x}{2^{n}}

= t a n x − t a n x 2 n = tanx - tan\frac{x}{2^{n}}

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paste it paste it

hi @Atul Solanki type this as in your question screen , latex seems attractive

sorry just apply } this sign at the last mathematical term

U Z - 6 years, 7 months ago

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