Given that α + β = 90⁰, show that √cosαcosecβ-cosαsinβ =sinα

Solution:

\( \\\sqrt{cos\alpha cosec\beta -cos\alpha sin\beta }=\sqrt{cos\alpha cosec(90^{0}-\alpha )-cos\alpha sin(90^{0}-\alpha)} \\ \\It\: is\: given\: that\: \alpha +\beta =90^{0} \\ \\=\sqrt{cos\alpha sec\alpha -cos\alpha cos\alpha } \\ \\We\: know\: that\: cos\alpha sec\alpha=1 \\ \\=\sqrt{1-cos^{2}\alpha } \\ \\=sin\alpha\ \)

Therefore, it is shown that \( \\\sqrt{cos\alpha cosec\beta -cos\alpha sin\beta }=sin\alpha\ \)

✦ Try This: Given that sinα = 1/2 and cosβ = 1/2 , then the value of (α + β) is a. 0°, b. 30°, c. 60°, d. 90°

☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 8

NCERT Exemplar Class 10 Maths Exercise 8.3 Sample Problem 3

Given that α + β = 90⁰, show that √cosαcosecβ-cosαsinβ =sinα

Summary:

Trigonometric ratios can be used to determine the ratios of any two sides out of a total of three sides of a right-angled triangle in terms of the respective angles. It is shown that √cosα cosecβ-cosα sinβ =sinα given α + β = 90⁰

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