Solve equation with sec/cosec/cot

A question is this type if and only if it requires solving an equation involving reciprocal trigonometric functions (sec, cosec, cot) that must be converted to sin/cos/tan and then solved using double or compound angle formulae.

3 questions · Moderate -0.1

1.05h Reciprocal trig functions: sec, cosec, cot definitions and graphs1.05j Trigonometric identities: tan=sin/cos and sin^2+cos^2=11.05o Trigonometric equations: solve in given intervals
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CAIE P2 2019 November Q6
9 marks Moderate -0.3
6
  1. Showing all necessary working, solve the equation $$\sec \alpha \operatorname { cosec } \alpha = 7$$ for \(0 ^ { \circ } < \alpha < 90 ^ { \circ }\).
  2. Showing all necessary working, solve the equation $$\sin \left( \beta + 20 ^ { \circ } \right) + \sin \left( \beta - 20 ^ { \circ } \right) = 6 \cos \beta$$ for \(0 ^ { \circ } < \beta < 90 ^ { \circ }\).
OCR C3 2014 June Q2
6 marks Standard +0.3
2 By first using appropriate identities, solve the equation $$5 \cos 2 \theta \operatorname { cosec } \theta = 2$$ for \(0 ^ { \circ } < \theta < 180 ^ { \circ }\).
OCR C3 Q5
7 marks Moderate -0.3
  1. Write down the identity expressing \(\sin 2\theta\) in terms of \(\sin \theta\) and \(\cos \theta\). [1]
  2. Given that \(\sin \alpha = \frac{1}{4}\) and \(\alpha\) is acute, show that \(\sin 2\alpha = \frac{1}{8}\sqrt{15}\). [3]
  3. Solve, for \(0° < \beta < 90°\), the equation \(5 \sin 2\beta \sec \beta = 3\). [3]