Question #dc76b

2 Answers
P dilip_k
Dec 9, 2017

#LHS=(1 + cotx)^2 + (1 - cotx)^2#
#=1 + cot^2x+2cotx + 1 +cot^2x- 2cotx#

#=2(1 + cot^2x)#
# = 2csc^2x=RHS#

Jim G.
Dec 9, 2017

#"see explanation"#

Explanation:

#"using the "color(blue)"trigonometric identity"#

#•color(white)(x)csc^2x=1+cot^2x#

#"consider the left side"#

#(1+cotx)^2+(1-cotx)^2larrcolor(blue)"expand factors"#

#=1cancel(+2cotx)+cot^2x+1cancel(-2cotx)+cot^2x#

#=2+2cot^2x#

#=2(1+cot^2x)#

#=2csc^2x="right side "rArr" verified"#

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