If sinθ=13/12, then what is the value of 26sinθ−10secθ?
Correct Answer:
D. −2
Explanation:
To solve for the value of 26sinθ - 10secθ, we first identify that if sinθ is 12/13, then cosθ can be found using the trigonometric identity sin²θ + cos²θ = 1, giving us cosθ = 5/13. Consequently, secθ, which is the reciprocal of cosθ, equals 13/5. By substituting these values into the expression, we get 26(12/13) - 10(13/5), which simplifies to 24 - 26, resulting in -2. This confirms that option D is the correct answer.
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