Summers Stephens
11/06/2023 · Junior High School
Simplify and write the trigonometric expression as a single squared trig function \( \frac{\sec t-\cos t}{\sec t}= \) Question Held: Worked Fxamnle
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Tutor-Verified Answer
Step-by-step Solution
Calculate or simplify the expression \( (\sec t-\cos t)/\sec t \).
Simplify the expression by following steps:
- step0: Solution:
\(\frac{\left(\sec\left(t\right)-\cos\left(t\right)\right)}{\sec\left(t\right)}\)
- step1: Remove the parentheses:
\(\frac{\sec\left(t\right)-\cos\left(t\right)}{\sec\left(t\right)}\)
- step2: Transform the expression:
\(\frac{\frac{1-\cos^{2}\left(t\right)}{\cos\left(t\right)}}{\sec\left(t\right)}\)
- step3: Transform the expression:
\(\frac{\frac{1-\cos^{2}\left(t\right)}{\cos\left(t\right)}}{\frac{1}{\cos\left(t\right)}}\)
- step4: Multiply by the reciprocal:
\(\frac{1-\cos^{2}\left(t\right)}{\cos\left(t\right)}\times \cos\left(t\right)\)
- step5: Reduce the fraction:
\(1-\cos^{2}\left(t\right)\)
- step6: Transform the expression:
\(1-\left(1-\sin^{2}\left(t\right)\right)\)
- step7: Calculate:
\(1-1+\sin^{2}\left(t\right)\)
- step8: Remove the opposites:
\(\sin^{2}\left(t\right)\)
The simplified form of the trigonometric expression \( \frac{\sec t-\cos t}{\sec t} \) as a single squared trig function is \( \sin^{2}(t) \).
Quick Answer
\( \sin^{2}(t) \)
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