Grade 1010 grade maths
ProveSin^a2+Cos^2a=1
Prove
Sin^a2+Cos^2a=1
4 Answers
lokesh
Approved Tutor Answer11 Years agosin(x)^2+cos(x)^2 = 1
cos(x)^2+sin(x)^2 = 1
cos(x)cos(x)+sin(x)sin(x) = 1
cos(x - x) = 1 ....
Note: I'm using the Sum-Difference Identity: cos(A - B) = cos(A)cos(B) + sin(A)sin(B)
cos( 0 ) = 1
1 = 1
cos(x)^2+sin(x)^2 = 1
cos(x)cos(x)+sin(x)sin(x) = 1
cos(x - x) = 1 ....
Note: I'm using the Sum-Difference Identity: cos(A - B) = cos(A)cos(B) + sin(A)sin(B)
cos( 0 ) = 1
1 = 1
Nikhil Gaddam
Thanks
Yash Baheti
Hi,
Take a right angled triangle.
Find the values of Sin and Cos in terms of , P, B, and H. Where P is perpendicular length, Bia base length and H is hypoteneous Length. Put the values in pythagoras theorem, you will get the identity.
Take a right angled triangle.
Find the values of Sin and Cos in terms of , P, B, and H. Where P is perpendicular length, Bia base length and H is hypoteneous Length. Put the values in pythagoras theorem, you will get the identity.
Yugabrat Gogoi
Please find your answer below.
we know that sin= (opposite line of a)/hypotenuse
so let sin be o/h
we know that cos=adjecent line to a/hypotenuse
so, let cos = a/h
sin2a+cos2a=1
lhs,
=(o/h)2+(a/h)2
=(o2+a2)/h2
=h2/h2 [lets take ‘o’ as ‘a’ , ‘a’ as ‘b’ and hypotenuse as ‘c’ by using =1 pytogorus theorum a2+b2=c2]
rhs
=1
therefore prooved sin2a+cos2a=1.
hope u like it .
regards Yugabrat Gogoi
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