if sec θx+,4xthen prove that sec θ + tan 8-2 r or

1.	if sec θx+,4xthen prove that sec θ + tan 8-2 r or
Answer» Let theta = A SecA=x+1/4x∴, sec²A=(x+1/4x)²=x²+2.x.1/4x+1/16x²=x²+1/2+1/16x² Now, sec²A-tan²A=1or, tan²A=sec²A-1or, tan²A=x²+1/2+1/16x²-1or, tan²A=x²+1/16x²-1/2or, tan²A=x²-2.x.1/4x+1/16x²or, tan²A=(x-1/4x)²or, tanA=+-(x-1/4x) Therefore, either secA+tanA=x+1/4x+x-1/4x [when tanA=x+1/4x]=2x or, secA+tanA=x+1/4x-x+1/4x [when tanA=-(x+1/4x)]=1/4x+1/4x=2/4x=1/2x (Proved)

Answer»

Let theta = A

SecA=x+1/4x∴, sec²A=(x+1/4x)²=x²+2.x.1/4x+1/16x²=x²+1/2+1/16x²

Now, sec²A-tan²A=1or, tan²A=sec²A-1or, tan²A=x²+1/2+1/16x²-1or, tan²A=x²+1/16x²-1/2or, tan²A=x²-2.x.1/4x+1/16x²or, tan²A=(x-1/4x)²or, tanA=+-(x-1/4x)

Therefore, either secA+tanA=x+1/4x+x-1/4x [when tanA=x+1/4x]=2x

or,

secA+tanA=x+1/4x-x+1/4x [when tanA=-(x+1/4x)]=1/4x+1/4x=2/4x=1/2x (Proved)

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