SSC CGL Tier II 12 Jan 2017 Paper 1

Question : 86 of 100

Marks: +1, -0

If secA + tanA = a, then the value of cosA is

Solution:

(2) secA + tanA = a ..... (i)
∵ sec

^{2}

A – tan

^{2}

A = 1
⇒ (secA + tanA) (secA – tanA) = 1
⇒ secA – tanA =

1/ a

... (ii)
On adding equations (i) and (ii),

2 \sec A=a+ {1}/{a}= {a^{2}+1}/{a}

⇒ \sec A= {a^{2}+1}/{2 a}

⇒ \cos A= {2 a}/{a^{2}+1}

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