verifying identities using fundamental identities?

Question

im having trouble grasping the concept of verifying identities...

1) (sinx) / (1+cosx ) + (sinx) / (1-cosx) = 2cscx

2) [(sinx + cosx) / sinx] + [(sinx - cosx) / cosx] = (cscx)(secx)

step by step explanations would be extremely helpful.

Answer 1

Prove the identity.

1) sinx / (1 + cosx ) + sinx / (1 - cosx) = 2cscx

Left Hand Side = sinx / (1 + cosx ) + sinx / (1 - cosx)

= sinx(1 - cosx) / [(1 + cosx )(1 - cosx)]
+ sinx(1 + cosx) / [(1 - cosx)(1 + cosx)]

= sinx(1 - cosx) / (1 - cos²x ) + sinx(1 + cosx) / (1 - cos²x )

= sinx(1 - cosx) / sin²x + sinx(1 + cosx) / sin²x

= (1 - cosx) / sinx + (1 + cosx) / sinx

= (1 - cosx + 1 + cosx) / sinx

= 2 / sinx = 2cscx = Right Hand Side
___________________

2) [(sinx + cosx) / sinx] + [(sinx - cosx) / cosx] = (cscx)(secx)

Left Hand Side = [(sinx + cosx) / sinx] + [(sinx - cosx) / cosx]

= [1 + (cosx / sinx)] + [(sinx / cosx) - 1]

= (cosx / sinx) + (sinx / cosx)

= cos²x / [(cosx)(sinx)] + sin²x / [(cosx)(sinx)]

= (cos²x + sin²x) / [(cosx)(sinx)]

= 1 / [(cosx)(sinx)] = (1/sinx)(1/cosx)

= (cscx)(secx) = Right Hand Side

Answer 2

instruct the identity. sin x + cot x cos x = csc x enable's commence with the left hand facet. Left Hand facet = sin x + cot x cos x = sin²x/sin x + (cos x/sin x) cos x = sin²x/sin x + cos²x/sin x = (sin²x + cos²x)/sin x = a million/sin x = csc x = suited Hand facet

Answer 3

sep ,19,1986