Solve with restricted domain

A question is this type if and only if it requires solving a trigonometric equation where the domain excludes certain values (e.g., θ ≠ 90n°) due to undefined reciprocal functions.

1 questions · Standard +0.3

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OCR H240/01 2021 November Q8
10 marks Standard +0.3
8 Functions f and g are defined for \(0 \leqslant x \leqslant 2 \pi\) by \(\mathrm { f } ( x ) = 2 \tan x\) and \(\mathrm { g } ( x ) = \sec x\).
    1. State the range of f .
    2. State the range of \(g\).
    1. Show that \(\operatorname { fg } ( 0.6 ) = 5.33\), correct to 3 significant figures.
    2. Explain why \(\mathrm { f } ^ { - 1 } \mathrm {~g} ( 0.6 )\) is not defined.
  3. In this question you must show detailed reasoning. Solve the equation \(( \mathrm { f } ( x ) ) ^ { 2 } + 6 \mathrm {~g} ( x ) = 0\).