Trig identities how does cos^2x become 1-sin

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How does cos^2x become 1-sin

Nov 20th, 2014

In trignometric functions

The cos,sin and tan are defined by ratios of base,altitude and hypotenuse in a right angled triangle

Let us say a=altitude



by pythgorean theorem

a^2+b^2=h^2 ---------------(1)

also we know cos is defined as ratio of base/hypotenuse so b/h

sin is defined as altitude/hypotenuse=a/h

DIVIDING EXPRESSION  (1) BY h^2 on both sides

we get

a^2/h^2  +b^2/h^2=h^2/h^2

(a/h)^2  +(b/h)^2=1 substituting a/h as sin and b/h as cos

sin^2x +cos^2x=1

From this relation we get cos^2x=1-sin^2x

Nov 20th, 2014

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