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If 2sinx +15cos^2x=7, find tanx.?
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If 2sinx +15cos^2x=7, find tanx.?
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If 2sinx +15cos^2x=7, find tanx.?
Solution:
Given equation: 2sinx - 15cos^2x = 7
Step 1: Rewrite the equation
2sinx - 15(1 - sin^2x) = 7
2sinx - 15 + 15sin^2x = 7
15sin^2x + 2sinx - 22 = 0
Step 2: Solve for sinx
Let y = sinx
15y^2 + 2y - 22 = 0
Using the quadratic formula,
y = (-2 ± sqrt(2^2 - 4*15*(-22))) / 2*15
y = (-2 ± sqrt(4 + 1320)) / 30
y = (-2 ± sqrt(1324)) / 30
y = (-2 ± 36.4) / 30
y = 1.21 or y = -1.54
Step 3: Find tanx
Since sinx = y,
sinx = 1.21 or sinx = -1.54
Since sinx lies in the range [-1, 1], sinx = 1.21 is not valid.
Therefore, sinx = -1.54
Now, tanx = sinx / cosx
cosx = sqrt(1 - sin^2x) = sqrt(1 - (-1.54)^2) = sqrt(1 - 2.3716) = sqrt(-1.3716) (which is not real)
Hence, there is no real solution for tanx.
Community Answer
If 2sinx +15cos^2x=7, find tanx.?
2sinx+15cos^x=7
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If 2sinx +15cos^2x=7, find tanx.?
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If 2sinx +15cos^2x=7, find tanx.? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about If 2sinx +15cos^2x=7, find tanx.? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If 2sinx +15cos^2x=7, find tanx.?.
If 2sinx +15cos^2x=7, find tanx.? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about If 2sinx +15cos^2x=7, find tanx.? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If 2sinx +15cos^2x=7, find tanx.?.
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