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Evaluate : (i) (sin18^@)/(cos72^@) ...

Evaluate :
(i) `(sin18^@)/(cos72^@)`
(ii) `(tan26^@)/(cot64^@)`
(iii) `cos48^@-sin42^@`
(iv) `c o s e c 31^@sec59^@`

Text Solution

AI Generated Solution

Let's evaluate the given expressions step by step. ### (i) Evaluate \( \frac{\sin 18^\circ}{\cos 72^\circ} \) 1. **Identify Complementary Angles**: Notice that \( 72^\circ + 18^\circ = 90^\circ \). Therefore, \( \sin 18^\circ \) can be rewritten using the complementary angle identity. 2. **Use Complementary Angle Identity**: We know that \( \sin(90^\circ - \theta) = \cos(\theta) \). Thus, \( \sin 18^\circ = \cos(72^\circ) \). ...
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