Trigonometry
posted by Fern Angel
Prove the following identities:
1. (tan theta  sin theta)^2 + (1cos theta)^2 = (1sec theta) ^2
2. (12cos^2 theta) / sin theta cos theta = tan theta  cot theta
3. (sin theta + cos theta ) ^2 + (sin theta  cos theta ) ^2 = 2
Thank you so much! :)

Steve
sinθ = tanθ cosθ, so
tanθ  sinθ = tanθ (1cosθ)
squared that is tan^2θ (1cosθ)^2
now we can add up the left side:
tan^2θ(1cosθ)^2 + (1cosθ)^2
= (tan^2θ + 1)(1cosθ)^2
= sec^2θ (1cosθ)^2
on the right side, we have
1secθ = (cosθ1)/cosθ
squared, that is sec^2θ (cosθ1)^2
and they are the same
Respond to this Question
Similar Questions

Algebra II
Which of the following expressions are not equal to 1? 
Calculus
I wanted to confirm that I solved these problems correctly (we had to convert the polar curves to Cartesian equations). 1.rcos(theta)=1 x=1 2.r=2*sin(theta)+2*cos(theta) r^2=2rsin(theta)+2rcos(theta) x^2+y^2=2y+2x (a little unsure … 
Algebra II
Multiple Choice Which expression is NOT equivalent to 1? 
Precalculus check answers help!
1.) Find an expression equivalent to sec theta sin theta cot theta csc theta. tan theta csc theta sec theta ~ sin theta 2.) Find an expression equivalent to cos theta/sin theta . tan theta cot theta ~ sec theta csc theta 3.) Simplify … 
Precalculus check answers help!
1.) Find an expression equivalent to sec theta sin theta cot theta csc theta. tan theta csc theta sec theta ~ sin theta 2.) Find an expression equivalent to cos theta/sin theta . tan theta cot theta ~ sec theta csc theta 3.) Simplify … 
trig
If sin theta is equal to 5/13 and theta is an angle in quadrant II find the value of cos theta, sec theta, tan theta, csc theta, cot theta. 
math
I have a question I have been working on since yesterday and I am not making this up. I couldn't get the right answer. If sin theta = 2/3, which of the following are possible? 
Trigonometry
Prove the following identities: 1. (tan theta  sin theta)^2 + (1cos theta)^2 = (1sec theta) ^2 2. (12cos^2 theta) / sin theta cos theta = tan theta  cot theta 3. (sin theta + cos theta ) ^2 + (sin theta  cos theta ) ^2 = 2 Thank … 
Precalculus
Circle O below has radius 1. Eight segment lengths are labeled with lowercase letters. Six of these equal a trigonometric function of theta. Your answer to this problem should be a six letter sequence whose letters represent the segment … 
math;)
Julia wants to simplify the term sec^2 theta1/cot^2 theta+1 in a trigonometric identity that she is proving. Which of the following identities should use to help her?