Q)

Asked by araima2001 | 29th Nov, 2016, 08:27: AM

Expert Answer:

we space know space that space sin space straight x degree space equals space sin left parenthesis 180 degree minus straight x degree right parenthesis
space we space will space be space using space this space formula space here. space
2 sin 2 degree space plus 4 sin 4 degree plus... plus 180 space sin 180 degree space equals 2 sin 2 degree space plus 4 sin 4 degree space plus.. plus 178 space sin space 178 degree plus 0... as space sin space 180 degree space equals 0

now space since space sin 2 degree space equals space sin space 178 degree comma space sin 4 degree space equals space sin 176 degree... space
we space get space given space expression space equals left parenthesis 2 sin 2 degree space plus 178 space sin 2 degree right parenthesis plus left parenthesis 4 space sin space 4 degree space plus space 176 space sin 4 degree right parenthesis space plus.... plus space left parenthesis 88 sin 88 degree plus 92 space sin 88 degree right parenthesis plus 90 sin space 90 degree
space equals 180 space sin space 2 degree plus 180 space sin 4 degree plus... plus 180 space sin space 88 degree plus plus 90 space........................ as space sin space 90 degree space equals 1
space equals 180 space left parenthesis sin 2 degree space plus sin 4 degree space plus... plus sin 88 degree right parenthesis plus 90
space equals 90 left square bracket left parenthesis 2 sin 1 degree space sin 2 degree plus 2 sin 1 degree space sin 4 degree plus... plus 2 sin 1 degree space sin 88 degree right parenthesis divided by sin 1 degree right square bracket plus 90
space equals 90 left curly bracket left square bracket left parenthesis cos 1 degree minus cos 3 degree right parenthesis plus left parenthesis cos 3 degree minus cos 5 degree right parenthesis plus... plus left parenthesis cos 87 degree minus cos 89 degree right parenthesis right square bracket divided by sin 1 degree right curly bracket plus 90
space equals 90 left square bracket left parenthesis cos 1 degree minus cos 89 degree right parenthesis divided by sin 1 degree right square bracket plus 90
space equals 90 left square bracket left parenthesis cos 1 degree divided by sin 1 degree right parenthesis minus left parenthesis cos 89 degree divided by sin 1 degree right parenthesis right square bracket plus 90 space space space space space space space space space

space but space cos 89 degree equals sin 1 degree

space so space given space expression space equals 90 left square bracket cot 1 degree minus left parenthesis sin 1 degree divided by sin 1 degree right parenthesis right square bracket plus 90
space equals 90 space cot 1 degree space minus 90 plus 90
space equals 90 space cot space 1 degree
equals 90 tan left parenthesis 90 degree minus 1 degree right parenthesis
equals 90 tan 89 degree

Answered by Vijaykumar Wani | 29th Nov, 2016, 11:22: AM

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