Add and subtract as indicated. Then simplify your answer if possible. Leave your answer in terms of sin(θ) and/or cos(θ).
sinθ+ 1/cosθ
Are you this poster?
http://www.jiskha.com/display.cgi?id=1327947103
sinØ + 1/cosØ
= (sinØcosØ + 1)/cosØ
actually the original looks more simple than this, and already is in terms of sines and cosines
To add and subtract the expression sinθ + 1/cosθ, we need to find a common denominator. The denominator of the second term is cosθ, so we'll multiply the first term sinθ by cosθ/cosθ to get a common denominator of cosθ:
(sinθ)(cosθ/cosθ) + 1/cosθ
This simplifies to:
(sinθ * cosθ + 1)/cosθ
Next, we simplify the numerator:
sinθ * cosθ + 1
To simplify further, we can use the trigonometric identity sinθ * cosθ = 1/2 * sin(2θ). So the expression becomes:
(1/2 * sin(2θ) + 1)/cosθ
Finally, we have simplified the expression sinθ + 1/cosθ to:
(1/2 * sin(2θ) + 1)/cosθ