Pregunta
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Responder
Both expressions simplify to
.
Solución
Let’s simplify both expressions step by step.
1. Simplifying
:
-
Adjust Angles to Standard Positions:
-
-
Substitute Known Values:
-
-
(since ) -
(since ) -
(since )
-
-
Substitute into the Expression:
-
Use Product-to-Sum Identity:
-
Simplify Further:Since
:
2. Simplifying
:
-
Adjust Angles to Standard Positions:
-
(since ) -
-
-
Apply the Difference of Squares Identity:Let
and :
Final Simplified Results:
Both expressions simplify to:
Respondido por UpStudy AI y revisado por un tutor profesional
Como
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Extra Insights
To simplify the given expression, we first deal with the individual components step-by-step.
Starting with the numerator:
-
-
because cosine is an even function. Hence, . - For
, we can express it as because cosine is also even. - Now, we simplify the angle of sine:
.
Putting this together, the numerator becomes:
Now for the denominator, we have
, which we can break down as:
Next, for the second part
:
-
(375 is 360 plus 15). -
as cosine is even.
Thus, we have:
Using the identity
, we simplify further.
Putting it all together gives us a refined and simplified expression without using any trigonometric identities requiring “a”.
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