In Exercises 1–60, verify each identity. tan x csc x cos x = 1

Video transcript

Hello, everybody I be doing today today we're going to put again this question that states determine the, whether the given identity is true or false where our given identity is sine squared, theta multiplied by COCA theta multiplied by CCAS theta. And that will be equal to tangent data. Now, we only have two answer choices A being true and B being false. Now, for a question like this, I usually like to tackle each side of the equation first. So an equation where or a question where I need to say if it's true or false, I tackle each side of the equation first. In this case, I just have to prove that the left hand side of our equation is equal to 10 in a theta. So I'm only gonna refer to the left hand side of our equation. So referring to that left hand side, the first thing I'll do is recall and I can recall that sequences of theta is equal to one divided by sine of theta. And I can also recall that see cans of theta is equal to one divided by cosine of theta. And now I can rewrite. So I have open parentheses, sine squared, theta closed parentheses multiplied by open parentheses. One divided by sine of theta closed parentheses multiplied by open parentheses, one divided by cosine of theta closed parentheses. Now, in this case, in my middle parentheses, the sign of the will cancel with one of the sine theta in the sine squared data. So I'll be left with open parentheses sin of theta multiplied by one multiplied by open parentheses. One divided by a cosine of data. Now, I can ignore the one because anything multiplied by one will be the same thing. So I can just multiply sine of data multiplied by one divided by cosine data which will give me sine of theta divided by a cosine of theta. And if I recall, I can say that tangent of theta is equal to sine of theta divided by cosine theta. So on the left hand side of our equation, we'll have tangents of theta and that'll be equal to the right hand side of our equation which was also tied in data. So this checks out both sides of the equation are equal to each other, which is answer to a true. So I hope that was helpful. And until next time.