Topic Details (Notes format)

How to Solve Advanced Trigonometric Equations (Using Identities)

Subject: Mathematics

Book: Maths Mastery

More complex trig equations involve identities (sin²x+cos²x=1, tan²x+1=sec²x) or transformations (e.g., rewriting sin(2x)=2sin(x)cos(x)). For instance, to solve sin(2x)=√3/2, replace sin(2x) with 2sin(x)cos(x) if needed, or interpret 2x angles. Factor or rearrange to isolate x. These equations appear in wave interference, engineering vibrations, or advanced geometry. Systematically applying identities and known angles ensures precise solutions across multiple intervals. Deep practice fosters agility in unraveling cyclical equations that drive modern science and technology.

Practice Questions

If a+b = 10 and ab = 21, what is the value of a^3 + b^3?

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A man rows downstream at 6 km/h and upstream at 4 km/h. What is the speed of the stream?

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The ratio of two numbers is 3:5, and their sum is 64. What are the numbers?

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The sum of the squares of two consecutive integers is 145. What are the integers?

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If the ratio of two numbers is 3:5 and their HCF is 4, what are the numbers?

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If sin(A) = 1/2 and A is acute, what is the value of A?

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How many ways can 4 people sit in a row?

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If sin(A) = 3/5 and cos(B) = 5/13, where A and B are acute angles, what is sin(A+B)?

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If two complementary angles differ by 30°, what are the angles?

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The sides of a triangle are 7, 24, and 25. Is this a right triangle?

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