To find the value of the expression tan 152° tan 62° / tan 242° + tan 28°, we can use trigonometric identities and the given information that tan 28° = n.
Let's break down the expression step by step:
1. First, note that tan 152° is equal to tan (180° - 28°). By using the identity tan (180° - x) = -tan x, we can rewrite tan 152° as -tan 28°.
2. Similarly, tan 242° can be rewritten as tan (180° + 62°) using the identity tan (180° + x) = -tan x. Thus, tan 242° is equal to -tan 62°.
3. Now, substitute these values and the given value of tan 28° = n into the expression:
(-tan 28° * tan 62°) / (-tan 242° + tan 28°)
4. Using the identity tan(-x) = -tan(x), we can simplify the expression further:
(-tan 28° * tan 62°) / (tan 242° - tan 28°)
5. Now, substitute the values of tan 28° = n and tan 242° = -tan (180° + 62°) = -tan 62° into the expression:
(-n * tan 62°) / (-tan 62° - n)
6. Finally, cancel out the common factor of -n:
-tan 62° / (tan 62° + n)
So, the value of the expression tan 152° tan 62° / tan 242° + tan 28° is *-tan 62° / (tan 62° + n)*.
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Step-by-step explanation:
To find the value of the expression tan 152° tan 62° / tan 242° + tan 28°, we can use trigonometric identities and the given information that tan 28° = n.
Let's break down the expression step by step:
1. First, note that tan 152° is equal to tan (180° - 28°). By using the identity tan (180° - x) = -tan x, we can rewrite tan 152° as -tan 28°.
2. Similarly, tan 242° can be rewritten as tan (180° + 62°) using the identity tan (180° + x) = -tan x. Thus, tan 242° is equal to -tan 62°.
3. Now, substitute these values and the given value of tan 28° = n into the expression:
(-tan 28° * tan 62°) / (-tan 242° + tan 28°)
4. Using the identity tan(-x) = -tan(x), we can simplify the expression further:
(-tan 28° * tan 62°) / (tan 242° - tan 28°)
5. Now, substitute the values of tan 28° = n and tan 242° = -tan (180° + 62°) = -tan 62° into the expression:
(-n * tan 62°) / (-tan 62° - n)
6. Finally, cancel out the common factor of -n:
-tan 62° / (tan 62° + n)
So, the value of the expression tan 152° tan 62° / tan 242° + tan 28° is *-tan 62° / (tan 62° + n)*.