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If it is ggiven that sin 2 x + 3cosx-2 = 0, then find the value of cos 3 x + sec 3 x
If it is ggiven that sin2x + 3cosx-2 = 0, then find the value of cos3x + sec3x


3 years ago

Arun
25768 Points
							Dear Studentsin^2x = 1 – cos^2 xnow1 – cos^2 x + 3 cos x – 2=0cos^2 x- 3cos x +1 = 0let cos x = tthen it will form a quadratic equationt^2 – 3t + 1 = 0t = (3 + $\sqrt$5)/2  and t = (3 –  $\sqrt$5)/21st value is cancellednow cos x= (3 –  $\sqrt$5)/2now you can easily find out the answer. regardsArun (askIITians forum expert)

3 years ago
Rishabh Sankla
33 Points
							Dear Student,Hope this will help you. $sin^2 x + 3 cos x = 2$ $\Rightarrow (1-cos^2 x) + 3 cos x = 2$ $\Rightarrow cos^2 x - 3 cos x = -1$                [After shifting terms] $\Rightarrow cos x(cos x - 3) = -1$ $\Rightarrow cos x - 3 = -sec x$ $\Rightarrow cos x + sec x = 3$ $\Rightarrow (cos x + sec x)^3 = (3)^3$ $\Rightarrow cos^3 x + sec^3 x + 3 cos x sec x(cos x + sec x) = 27$ $\Rightarrow cos^3 x + sec^3 x + 3\times3 = 27$ $\Rightarrow cos^3 x + sec^3 x = 18$ This is the simpler method to find answer to this question. RegardsRishabh

one year ago
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### Course Features

• 31 Video Lectures
• Revision Notes
• Test paper with Video Solution
• Mind Map
• Study Planner
• NCERT Solutions
• Discussion Forum
• Previous Year Exam Questions