Question:
Find the value of
\[
\sin 70^\circ \left( \cot 10^\circ \cot 70^\circ - 1 \right).
\]
Find the value of
\[
\sin 70^\circ \left( \cot 10^\circ \cot 70^\circ - 1 \right).
\]
Show Hint
Use trigonometric identities to simplify expressions. In this case, the product \( \cot 10^\circ \cot 70^\circ = 1 \) simplifies the calculation.
Updated On: Mar 8, 2025
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Solution and Explanation
Using trigonometric identities:
- We know that \( \cot 10^\circ \cot 70^\circ = 1 \) (since \( \cot \theta \cot (90^\circ - \theta) = 1 \)).
- Therefore, the expression becomes:
\[
\sin 70^\circ \left( 1 - 1 \right) = 0.
\]
Thus, the value of the expression is 0.
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