Class 10 Maths Chapter 9 Important Questions Introduction to Trigonometry


Important questions for Introduction to Trigonometry Chapter 9 Class 10 Maths with solutions. Extra questions for class 10 Maths Chapter 9.


    Q1:

    Prove that: \(\frac{sinθ}{1 + cosθ}\) + \(\frac{1 + cosθ}{sinθ}\) = 2 cosecθ

    CBSE [2023]

    Easy

    Q2:

    Prove that: \(\frac{1 + secA}{secA}\) = \(\frac{sin²A}{1 - cosA}\)

    CBSE [2023]

    Easy

    Q3:

    Prove that: \(\frac{tanθ}{1 - cotθ}\) + \(\frac{cotθ}{1 - tanθ}\) = 1 + secθcosecθ

    CBSE [2023]

    Medium

    Q4:

    Prove that: \(\sqrt{\frac{secA - 1}{secA + 1}}\) + \(\sqrt{\frac{secA + 1}{secA - 1}}\) = 2cosecA

    CBSE [2023]

    Medium

    Q5:

    If acosθ + bsinθ = m and asinθ - bcosθ = n, then prove that a² + b² = m² + n².

    CBSE [2023]

    Medium

    Q6:

    Prove that: secA (1 – sin A) (sec A + tan A) = 1.

    CBSE [2023]

    Medium

    Q7:

    Prove that: \(\frac{sinA - 2sin³A}{2cos³A - cosA}\) = tanA

    CBSE [2023]

    Medium

    Q8:

    If A and B are acute angles such that sin (A – B) = 0 and 2 cos (A + B) – 1 = 0, then find angles A and B.

    CBSE [2023]

    Easy

    Q9:

    Evaluate: \(\frac{5cos²60° + 4sec²30° - tan²45°}{sin²30° + cos²30°}\)

    CBSE [2023]

    Easy

    Q10:

    secθ when expressed in terms of cotθ, is equal to: (a) \(\frac{1 + cot²θ} {cotθ}\) (b) \(\sqrt{1 + cot²θ}\) (c) \(\frac{\sqrt{1 + cot²θ}}{cotθ}\) (d) \(\frac{\sqrt{1 - cot²θ}}{cotθ}\)

    CBSE [2023]

    Easy

    Q11:

    Prove that: (\(\frac{1}{cosθ}\) - \(\cosθ\)) (\(\frac{1}{sinθ}\) - \(\sinθ\)) = \(\frac{1}{tanθ + cotθ}\)

    CBSE [2023]

    Easy

    Q12:

    If cosA + cos²A = 1, then find the value of sin²A + sin⁴A.

    CBSE [2023]

    Easy

    Q13:

    If 4cot²45° - sec²60° + sin²60° + p = \(\frac{3}{4}\), then find the value of p.

    CBSE [2023]

    Easy

    Q14:

    Prove: \(\frac{tanθ + secθ - 1}{tanθ - secθ + 1}\) = \(\frac {1 + sinθ}{cosθ}\)

    CBSE [2023]

    Easy

    Q15:

    If sinα = \(\frac{1}{√2}\) and cotβ = √3, then find the value of cosecα + cosecβ

    CBSE [2023]

    Easy

    Q16:

    If sinθ + cosθ = \(\sqrt{3}\), then find the value of sinθ × cosθ

    CBSE [2023]

    Easy

    Q17:

    If 2tanA = 3, then find the value of \(\frac{4sinA + 3cosA}{4sinA - 3cosA}\)

    CBSE [2023]

    Easy

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