Verify that each equation is an identity.
sin² θ (1 + co...

Question

Verify that each equation is an identity.

sin² θ (1 + cot² θ) - 1 = 0

Accepted Answer

Hello, everyone we are asked is the given equation in identity. We are given the equation cosine squared X multiplied by one plus the tangent squared of X closed parentheses minus one equals zero. Our answer choices are a yes B no. For this to be an identity, we need to make the left hand side equal the right hand side. So I'm going to start with the left hand side and we have the cosine squared of X multiplied by one plus the tangent squared of X closed parentheses minus one. So I will be distributing this into the parentheses. So the cosine squared of X will be distributed into our parentheses and we'll have cosine squared X plus cosine squared X tangent squared X minus one from there. I recall that I have an identity that states that the tangent squared of X is equal to the sine squared of X divided by the cosine squared of X. So I'm gonna substitute that in. So I have cosine squared X plus the cosine squared of X which will now be multiplied by the sine squared of X divided by the cosine squared of X closed parentheses. Still minus one when I multiply the cosine squared of X by the sine squared of X divided by cosine squared of X, I can cross reduce the cosine squared of X. So I get the cosine squared X plus sine squared X minus one. And we want this to equal zero. And we're almost there because the next identity I recall having was one that stated that the cosine squared of X plus the sine squared of X equals one. So if I substitute one in for the cosine squared of X plus sine squared of X, I'll get one minus one which equals zero. And that's what we wanted it to equal for it to be an identity. So this is answer choice. A yes, it is an identity. Have a nice day.

Struggling with Trigonometry?

Verify that each equation is an identity.
sin² θ (1 + cot² θ) - 1 = 0

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Introduction to Trigonometric Identities practice set

Struggling with Trigonometry?

Verify that each equation is an identity.sin² θ (1 + cot² θ) - 1 = 0

Watch next

Introduction to Trigonometric Identities practice set

Verify that each equation is an identity.
sin² θ (1 + cot² θ) - 1 = 0