Question

show that cosec2x+cosec4x+cosec8x+cosec16x+cosec32x=cotx - cot32x.

Answer 1

cosec(2x+4x+8x+16x+32x)
cosec(52)=cotx-cot32
cosec(52)=cot(x-32)
cosec(52)≠cot(-31)

Answer 2

Answer:

$\huge\colorbox{CYAN}{ANSWER}$

SHOW THAT COSEC2X+COSEC4X+COSEC8X+COSEC16X+COSEC32X=COTX–COT32X

COSECX+COTX=1/SINX+COSX/SINX

=1+COSX/SINX

WE CAN WRITE AS

2COS2X/2//2SINX/2COSX/2

$\huge\fbox{HERE WE KNOW THAT FORMULA IS =COSX=2COS²X/2–1 =COSX+1=2COS2X/2}$

=COSX/2//SINX/2=COTX/2

COSEC X+COTX=COTX/2

COSECX=COTX/2–COTX

COSEC2X+2X=1+COT²2X/SIN2X

=2COS²X/2SINXCOSX=COSX

COSEC 2X=COTX–COT2X —> EQ 1

COSEC4X=COT2X–COT4X—> EQ 2

COSEC 8X=COT4X–COT8X —> EQ 3

COSEC 16X=COT8X–COT16X —> EQ 4

COSEC 32X=COT16X–COT32X —> EQ 5

1+2+3+4+5

COSEC2X+4X+8X+16X+COSEC32X=COTX–COT32X