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sqrt(1+sinA)=-(sinA/2+cosA/2) is true if...

`sqrt(1+sinA)=-(sinA/2+cosA/2)` is true if

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(1+sinA-cosA)/(1+sinA+cosA)=

((2sinA) (1+ sinA))/(1+ sinA +cosA) is equal to : ((2sinA) (1+ sinA))/(1+ sinA +cosA) बराबर है:

(1-sinA+cosA)^(2) is equal to ?

((2sinA)(1+sinA))/(1+sinA+cosA) is equal to:

((2sinA)(1+sinA))/(1+sinA+cosA) is equal to:

Prove that sqrt((1+sinA)/(1-sinA))=(1+sinA)/cosA .

(sinA+cosA)^2+(sinA-cosA)^2=

Prove that: cotA/2-tanA/2=(cosA/2)/(sinA/2)-(sinA/2)/(cosA/2) =(cos^(2)A/2-sin^(2)A/2)/(sinA/2cosA/2) =cosA/(1/2.(2sinA/2cosA/2)) =(2cosA)/(sinA)=2cotA = RHS. Hence Proved.

Prove that: cotA/2-tanA/2=(cosA/2)/(sinA/2)-(sinA/2)/(cosA/2) =(cos^(2)A/2-sin^(2)A/2)/(sinA/2cosA/2) =cosA/(1/2.(2sinA/2cosA/2)) =(2cosA)/(sinA)=2cotA = RHS. Hence Proved.