Question

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Answer 1

Answer:

Proof in explanation.

Step-by-step explanation:

To prove: $sin^{2}$Ф + $cos^{2}$Ф = 1

Assumption: Let there be Right angled triangle with onle of the angles Ф

Let p= length of the perpendicular

b= length of the base

h= length of the hypotenuse

Proof:

We know that sinФ = p/h

and cosФ= b/h

So, $sin^{2}$Ф + $cos ^{2}$Ф = $(\frac{p}{h} )^{2} + (\frac{b}{h} )^{2}$

      $sin^{2}$Ф + $cos ^{2}$Ф= $\frac{p^{2} + b^{2}}{h^2}$

But, a/c Pythagoras theorem, $p^{2} + b^{2} = h^{2}$

So,  $sin^{2}$Ф + $cos ^{2}$Ф = $h^{2}$/$h^{2}$

Hence,  $sin^{2}$Ф + $cos ^{2}$Ф=1

Proved!

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