it says to verify the following identity, working only on one side:
cotx+tanx=cscx*secx
Work the left side.
cot x + tan x = cos x/sin x + sin x/cos x
= (cos^2 x +sin^2x)/(sin x cos x)
= 1/(sin x cos x)
= 1/sin x * 1/cos x
You're almost there.
thanks so much! i could not figure that one out!
but i did now, lol.
Great job figuring it out! It looks like you made a minor mistake in your simplification. Let me guide you through the correct steps:
Starting with the left side:
cot x + tan x = cos x/sin x + sin x/cos x
To obtain a common denominator, multiply the first fraction by cos x/cos x and the second fraction by sin x/sin x:
= (cos x * cos x)/(sin x * cos x) + (sin x * sin x)/(sin x * cos x)
Combine the fractions:
= (cos^2 x +sin^2 x)/(sin x * cos x)
Now, recognize that cos^2 x + sin^2 x equals 1 (as it is one of the fundamental identities of trigonometry):
= 1/(sin x * cos x)
And finally, simplify further by recognizing that 1/(sin x * cos x) can be expressed as csc x * sec x:
= csc x * sec x
So, the simplified left side equals the right side of the identity, verifying the given identity:
cot x + tan x = csc x * sec x
Keep up the good work! If you have any more questions or need further assistance, feel free to ask.