Question

prove the following identities:

(1 - sinA - cosA)²= 2(1-sinA) (1-cosA)

really need help

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Answer 1

Answer:

open (1-sinA-cosA)^2

Step-by-step explanation:

LHS=

$1^{2} +sinA^{2}+cosA^{2}-2(1)(sinA)+2(sinA)(cosA)-2(1)(cosA)\\because {(a+b+c)=a^{2}+b^{2} +c^{2} -2ab+2bc-2ca}$

1 +   1  -2sinA   +2(sinA)(cosA)   -2cosA

because sinA2+cosA2=1

taking 2 out as common

2 {1-sinA+(sinA)(cosA)-cosA}

Since $(x+a)(x+b)=x^{2} +(a+b)x+ab$

2(1-sinA)(1-cosA)

LHS=RHS

HENCE PROVED