secA (1-sina) (secA + tanA)=1
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secA (1-sinA) (secA + tan A)
secA (1-sinA) (secA + tan A) = (secA-sinA×secA)(secA+tanA)
secA (1-sinA) (secA + tan A) = (secA-sinA×secA)(secA+tanA)=(secA-tanA) (secA+tanA) as secA=1/cosA and sinA/cosA=tanA
secA (1-sinA) (secA + tan A) = (secA-sinA×secA)(secA+tanA)=(secA-tanA) (secA+tanA) as secA=1/cosA and sinA/cosA=tanA= (sec²A-tan²A) as (a+b)(a-b)=a²-b²
secA (1-sinA) (secA + tan A) = (secA-sinA×secA)(secA+tanA)=(secA-tanA) (secA+tanA) as secA=1/cosA and sinA/cosA=tanA= (sec²A-tan²A) as (a+b)(a-b)=a²-b²=sec²A-tan²A=1 from identity.
secA (1-sinA) (secA + tan A) = (secA-sinA×secA)(secA+tanA)=(secA-tanA) (secA+tanA) as secA=1/cosA and sinA/cosA=tanA= (sec²A-tan²A) as (a+b)(a-b)=a²-b²=sec²A-tan²A=1 from identity.Hence proved.
secA (1-sinA) (secA + tan A) = (secA-sinA×secA)(secA+tanA)=(secA-tanA) (secA+tanA) as secA=1/cosA and sinA/cosA=tanA= (sec²A-tan²A) as (a+b)(a-b)=a²-b²=sec²A-tan²A=1 from identity.
Hence proved.Hope this helps you .