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Trigonometry Identities - Tan^2 and Sec^2 to Identity (Greek Letter)

Level 1

This math topic focuses on mastering the use of trigonometric identities involving the functions tangent (tan) and secant (sec). Learners are challenged to manipulate expressions with these functions and rewrite them using Pythagorean identities, mainly converting tan² and sec² expressions into alternative trigonometric forms. This involves using identities that may incorporate sine (sin) and cosine (cos), other Pythagorean identities, and different algebraic forms to represent the same trigonometric expressions.

Work on practice problems directly here, or download the printable pdf worksheet to practice offline.

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Trigonometry Identities - Tan^2 and Sec^2 to Identity (Greek Letter) Worksheet

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Trigonometry Identities - Tan^2 and Sec^2 to Identity (Greek Letter)
1
A LaTex expression showing \text{cos} to the power of 2 {(\beta)}
Complete the pythagorean trig identity for this expression
a A LaTex expression showing =\frac{\text{tan} to the power of 2 {(\beta)}}{\text{sin} to the power of 2 {(\beta)}}
b A LaTex expression showing =\frac{\text{sin} to the power of 2 {(\beta)}}{\text{tan} to the power of 2 {(\beta)}}
2
A LaTex expression showing \text{sin} to the power of 2 {(\gamma)}
Complete the pythagorean trig identity for this expression
a A LaTex expression showing =\text{tan} to the power of 2 {(\gamma)} times \text{cos} to the power of 2 {(\gamma)}
b A LaTex expression showing =\frac{\text{cos} to the power of 2 {(\gamma)}}{\text{tan} to the power of 2 {(\gamma)}}
3
A LaTex expression showing \text{sin} to the power of 2 {(\theta)}
Complete the pythagorean trig identity for this expression
a A LaTex expression showing =\frac{\text{cos} to the power of 2 {(\theta)}}{\text{tan} to the power of 2 {(\theta)}}
b A LaTex expression showing =\text{tan} to the power of 2 {(\theta)} times \text{cos} to the power of 2 {(\theta)}
4
A LaTex expression showing \text{tan} to the power of 2 {(\theta)}
Complete the pythagorean trig identity for this expression
a A LaTex expression showing =\text{csc} to the power of 2 {(\theta)} - 1
b A LaTex expression showing =\text{sec} to the power of 2 {(\theta)} - 1
5
A LaTex expression showing \text{sec} to the power of 2 {(\theta)}
Complete the pythagorean trig identity for this expression
a A LaTex expression showing =\text{tan} to the power of 2 {(\theta)} - 1
b A LaTex expression showing =\text{tan} to the power of 2 {(\theta)} + 1
6
A LaTex expression showing \text{cos} to the power of 2 {(\gamma)}
Complete the pythagorean trig identity for this expression
a A LaTex expression showing =\frac{\text{sin} to the power of 2 {(\gamma)}}{\text{tan} to the power of 2 {(\gamma)}}
b A LaTex expression showing =\text{sin} to the power of 2 {(\gamma)} times \text{tan} to the power of 2 {(\gamma)}
7
A LaTex expression showing \text{tan} to the power of 2 {(\gamma)}
Complete the pythagorean trig identity for this expression
a A LaTex expression showing =\frac{\text{sin} to the power of 2 {(\gamma)}}{\text{cos} to the power of 2 {(\gamma)}}
b A LaTex expression showing =\text{sin} to the power of 2 {(\gamma)} - \text{cos} to the power of 2 {(\gamma)}
8
A LaTex expression showing \text{sec} to the power of 2 {(\alpha)}
Complete the pythagorean trig identity for this expression
a A LaTex expression showing =\text{tan} to the power of 2 {(\alpha)} - 1
b A LaTex expression showing =\text{tan} to the power of 2 {(\alpha)} + 1