Albert wants to show that tan theta sin theta cos theta se

Albert wants to show that tan theta sin theta + cos theta = sec theta He writes the following proof tan theta sin theta +cos theta = sec theta sin theta/cos theta sin theta + cos theta = sec theta sin^2 theta/cos theta + cos theta = sec theta What is the next step in this proof? He should write tan theta = sin theta/cos theta to find a common demoninator. He should write cos theta = cos^2 theta/cos theta to find a common denominator. He should write cos theta = 1- sin theta to convert all the terms to sine. He should write sin theta = 1-cos theta to convert all the terms to cosine How can Jamie rewrite the expression 1/1 - sin theta so that the fraction has cos^2 theta in the denominator? She can multiply the numerator and denominator by cos theta.

Solution

4) prove tan@*sin@ + cos@ = sec @

LHS:

tan@*sin@ + cos@

(sin@ / cos@)*sin@ + cos@

(sin²@ / cos@ ) + cos@

( sin² @ + cos²@ ) / cos@

[ use identity  sin² @ + cos²@ = 1]

1/ cos@ = sec@

= RHS

hence proved

that means he should write cos@ = cos² @ / cos@ to find common denominator.