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This is a PDF of class 11th trigonometry formulas for class 11th students in CBSE and other boards.
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Some examples from this set of practice questions
1.
### Question: Using the double angle formula for sine, calculate \\(\\sin 2A\\) if \\(\\sin A = \\frac{3}{5}\\) and \\(A\\) is in the first quadrant.
Answer: Given \\(\\sin A = \\frac{3}{5}\\) and knowing \\(A\\) is in the first quadrant, we can find \\(\\cos A\\) using the Pythagorean identity. 1. First, find \\(\\cos A\\): \\[ \\sin^2 A + \\cos^2 A = 1 \\] \\[ \\left(\\frac{3}{5}\\right)^2 + \\cos^2 A = 1 \\] \\[ \\frac{9}{25} + \\cos^2 A = 1 \\] \\[ \\cos^2 A = 1 - \\frac{9}{25} \\] \\[ \\cos^2 A = \\frac{25}{25} - \\frac{9}{25} \\] \\[ \\cos^2 A = \\frac{16}{25} \\] \\[ \\cos A = \\sqrt{\\frac{16}{25}} = \\frac{4}{5} \\] Since \\(A\\) is in the first quadrant, \\(\\cos A\\) is positive, so \\(\\cos A = \\frac{4}{5}\\). 2. Now, use the double angle formula for sine: \\[ \\sin 2A = 2 \\sin A \\cos A \\] Substitute the values: \\[ \\sin 2A = 2 \\left(\\frac{3}{5}\\right) \\left(\\frac{4}{5}\\right) \\] \\[ \\sin 2A = 2 \\left(\\frac{12}{25}\\right) \\] \\[ \\sin 2A = \\frac{24}{25} \\] Thus, \\(\\sin 2A = \\frac{24}{25}\\).
2.
Prove that \\(\\sin(A + B) = \\sin A \\cos B + \\cos A \\sin B\\).
Answer: Using the angle addition formula for sine, we have: \\[\\sin(A + B) = \\sin A \\cos B + \\cos A \\sin B\\] This is a standard trigonometric identity.
3.
Simplify \\(\\sec^2 x - \\tan^2 x\\).
Answer: Using the Pythagorean identity: \\[\\sec^2 x - \\tan^2 x = 1\\]
4.
If \\(\\sin \\theta = \\frac{3}{5}\\), find \\(\\cos \\theta\\).
Answer: Using \\(\\sin^2 \\theta + \\cos^2 \\theta = 1\\), \\[\\left(\\frac{3}{5}\\right)^2 + \\cos^2 \\theta = 1\\] \\[\\frac{9}{25} + \\cos^2 \\theta = 1\\] \\[\\cos^2 \\theta = 1 - \\frac{9}{25} = \\frac{16}{25}\\] \\[\\cos \\theta = \\pm \\frac{4}{5}\\]
5.
Prove that \\(\\cos(A - B) = \\cos A \\cos B + \\sin A \\sin B\\).
Answer: Using the angle subtraction formula for cosine, we have: \\[\\cos(A - B) = \\cos A \\cos B + \\sin A \\sin B\\] This is another standard trigonometric identity.
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