Express `"cosec"48^(@)+tan88^(@)` in terms of trigonometric ratios of angle between `0^(@)and45^(@)`.

Answer

To express \( \csc 48^\circ + \tan 88^\circ \) in terms of trigonometric ratios of angles between \( 0^\circ \) and \( 45^\circ \), we can use the complementary angle identities.

### Step 1: Express \( \csc 48^\circ \)
Using the complementary angle identity, we know that:
\[ \csc(90^\circ - \theta) = \sec(\theta) \]
For \( \csc 48^\circ \):
\[ \csc 48^\circ = \csc(90^\circ - 42^\circ) = \sec 42^\circ \]

### Step 2: Express \( \tan 88^\circ \)
Similarly, we can express \( \tan 88^\circ \) using the complementary angle identity:
\[ \tan(90^\circ - \theta) = \cot(\theta) \]
For \( \tan 88^\circ \):
\[ \tan 88^\circ = \tan(90^\circ - 2^\circ) = \cot 2^\circ \]

### Step 3: Combine the results
Now we can combine both results:
\[ \csc 48^\circ + \tan 88^\circ = \sec 42^\circ + \cot 2^\circ \]

### Final Answer
Thus, we have expressed \( \csc 48^\circ + \tan 88^\circ \) in terms of trigonometric ratios of angles between \( 0^\circ \) and \( 45^\circ \):
\[ \csc 48^\circ + \tan 88^\circ = \sec 42^\circ + \cot 2^\circ \]

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