Question

prove that sin square A+ cos square A=1

Answer 1

Hey !!!

we know that

h² = b² + p² -------1)

heighpotenius = base² + perpendicular²

we also know that

sin¢ = p/h

cos¢ = b/h

so , sin²¢ + cos²¢

(p/h )² + (b/h )²

=> b² + p² /h²

= h²/h² (from equation 1st)

= 1
._____________
2nd method

sin²¢ + cos²¢

1 - cos²¢ + cos²¢ ✔•°• sin²¢ = 1 - cos²¢

= 1 prooved

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Hope it helps you !!

@Rajukumar111

Answer 2

To Prove: sin² A  + cos² A  =1 
_____________________________

Proof:- 

⇒ Sin² A = $( \frac{perpendicular}{hypotenuse} )^2$

⇒ Cos² A = $( \frac{base}{hypotenuse} )^2$

-------------------------------------------------
L.H.S

Sin A + Cos A 

⇒ $\frac{perpendicular^2}{hypotenuse^2}) + \frac{base^2}{hypotenuse^2}$

⇒ $\frac{perpendicular^2 + base^2}{hypotenuse^2}$

⇒ $\frac{hypotenuse^2}{hypotenuse^2}$                      [tex][By Pythagoras theorem, base^2 + perpendicular^2 = hypotenuse^2 ][/tex]

⇒ 1

-----------------------------------

R.H.S

⇒ 1 

______________________________


Now,

1 = 1 

L.H.S = R.H.S



Hence, proved that sin²A + cos²A = 1


i hope this will help you


-by ABHAY