Write each expression in terms of sine and​ cosine, and then simplify so that no quotients appear in the final expression and all functions

Question

Write each expression in terms of sine and​ cosine, and then simplify so that no quotients appear in the final expression and all functions are of

theta

only.

StartFraction secant squared left parenthesis negative theta right parenthesis minus 1 Over 1 minus sine squared left parenthesis negative theta right parenthesis EndFraction

in progress 0
Alexandra 2 weeks 2021-09-12T03:34:53+00:00 1 Answer 0

Answers ( )

    0
    2021-09-12T03:36:20+00:00

    Answer:

    sec^2\theta\cdot tan^2\theta

    Step-by-step explanation:

    Trigonometric Functions

    There are some basic relations between the trigonometric functions that allow us to transform and conveniently manage them if many different ways. Some basic identities are:

    sin^2\theta+cos^2\theta=1

    sin(-\theta)=-sin\theta

    cos(-\theta)=cos\theta

    \displaystyle sec\theta=\frac{1}{cos\theta}

    sec(-\theta)=sec\theta

    We are required to simplify the following expression:

    \displaystyle \frac{sec^2(-\theta)-1}{1-sin^2(-\theta)}

    Transforming the negative arguments

    \displaystyle \frac{sec^2\theta-1}{1-sin^2\theta}

    Transforming the secant into cosine

    \displaystyle \frac{\frac{1}{cos^2\theta}-1}{1-sin^2\theta}

    Operating

    \displaystyle \frac{1}{cos^2\theta}\cdot \frac{1-cos^2\theta}{1-sin^2\theta}

    Applying the basic identity in the numerator and denominator

    \displaystyle \frac{1}{cos^2\theta}\cdot \frac{sin^2\theta}{cos^2\theta}

    Since

    \displaystyle tan\theta=\frac{sin\theta}{cos\theta}

    \boxed{sec^2\theta\cdot tan^2\theta}

Leave an answer

45:7+7-4:2-5:5*4+35:2 =? ( )