Write the left side of the identity in terms of sine and cosine. Rewrite the numerator and denominator separately. ​(Do not​ simplify.) Simp

Question

Write the left side of the identity in terms of sine and cosine. Rewrite the numerator and denominator separately. ​(Do not​ simplify.) Simplify the fraction from the previous step such that both the fractions have the common denominator The expression from the previous step then simplifies to using​ what? A. Addition and a Reciprocal Identity B. Addition and a Pythagorean Identity

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Thu Thủy 3 years 2021-07-23T18:42:42+00:00 1 Answers 28 views 0

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  1. sori
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    2021-07-23T18:43:59+00:00
    Reply

    Answer:

    (a) \frac{2}{cos\theta}/\frac{1}{sin\theta} + \frac{4sin\theta}{cos\theta} =6tan\theta

    (b) \frac{2sin\theta}{cos\theta} + \frac{4sin\theta}{cos\theta} =6tan\theta

    (c) Addition and Quotient identity

    Step-by-step explanation:

    Given

    \frac{2sec\theta}{csc\theta} + \frac{4sin\theta}{cos\theta} =6tan\theta — The expression missing from the question

    Solving (a): Write the left hand side in terms of sin and cosine

    In trigonometry:

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

    and

    csc\theta = \frac{1}{sin\theta}

    So, the expression becomes:

    \frac{2 * \frac{1}{cos\theta}}{\frac{1}{sin\theta}} + \frac{4sin\theta}{cos\theta} =6tan\theta

    \frac{\frac{2}{cos\theta}}{\frac{1}{sin\theta}} + \frac{4sin\theta}{cos\theta} =6tan\theta

    Rewrite as:

    \frac{2}{cos\theta}/\frac{1}{sin\theta} + \frac{4sin\theta}{cos\theta} =6tan\theta

    Solving (b): Simplify

    \frac{2}{cos\theta}/\frac{1}{sin\theta} + \frac{4sin\theta}{cos\theta} =6tan\theta

    Change / to *

    \frac{2}{cos\theta}*\frac{sin\theta}{1} + \frac{4sin\theta}{cos\theta} =6tan\theta

    \frac{2sin\theta}{cos\theta} + \frac{4sin\theta}{cos\theta} =6tan\theta

    Solving (c): The property used

    To do this, we need to further simplify

    \frac{2sin\theta}{cos\theta} + \frac{4sin\theta}{cos\theta} =6tan\theta

    Take LCM

    \frac{2sin\theta+ 4sin\theta}{cos\theta} =6tan\theta

    Add the numerator

    \frac{6sin\theta}{cos\theta} =6tan\theta

    Apply quotient identity

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

    This gives

    \frac{6sin\theta}{cos\theta} = 6tan\theta

    Hence, the properties applied are:

    Addition and Quotient identity

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