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If tan 25 degree= a, then what is tge value of tan205-tan115/tan245 tan335 in terms of a?
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If tan 25 degree= a, then what is tge value of tan205-tan115/tan245 ta...
Solution:
Step 1: Calculate tan 205 degree and tan 115 degree using the formula tan(180 + θ) = - tan θ.
tan 205 degree = tan(180 + 25) degree = -tan 25 degree = -a
tan 115 degree = tan(180 - 65) degree = -tan 65 degree
Step 2: Simplify the numerator and denominator of the expression tan205-tan115/tan245 tan335 using the formula for the difference of two tan values.
tan205 - tan115 = tan(205 - 115) degree / (1 + tan205 tan115) = tan90 degree / (1 + (-a)(-tan 65 degree)) = 1 / (1 + a tan 65 degree)
tan245 tan335 = tan(245 + 335) degree = tan580 degree = tan(360 + 220) degree = tan220 degree
tan245 tan335 = tan(245 + 335) degree = tan580 degree = tan(360 + 220) degree = tan220 degree
Step 3: Replace tan 65 degree and simplify the expression.
tan205 - tan115/tan245 tan335 = (1 / (1 + a tan 65 degree)) / (tan220 degree) = (1 / (1 + a (1/tan 25 degree))) / (tan220 degree)
= (1 / (1 + a (1/0.4663))) / (-0.7265)
= -1.4503 / (1 + 2.1441a)
Therefore, the value of tan205 - tan115/tan245 tan335 in terms of a is -1.4503 / (1 + 2.1441a).
Step 1: Calculate tan 205 degree and tan 115 degree using the formula tan(180 + θ) = - tan θ.
tan 205 degree = tan(180 + 25) degree = -tan 25 degree = -a
tan 115 degree = tan(180 - 65) degree = -tan 65 degree
Step 2: Simplify the numerator and denominator of the expression tan205-tan115/tan245 tan335 using the formula for the difference of two tan values.
tan205 - tan115 = tan(205 - 115) degree / (1 + tan205 tan115) = tan90 degree / (1 + (-a)(-tan 65 degree)) = 1 / (1 + a tan 65 degree)
tan245 tan335 = tan(245 + 335) degree = tan580 degree = tan(360 + 220) degree = tan220 degree
tan245 tan335 = tan(245 + 335) degree = tan580 degree = tan(360 + 220) degree = tan220 degree
Step 3: Replace tan 65 degree and simplify the expression.
tan205 - tan115/tan245 tan335 = (1 / (1 + a tan 65 degree)) / (tan220 degree) = (1 / (1 + a (1/tan 25 degree))) / (tan220 degree)
= (1 / (1 + a (1/0.4663))) / (-0.7265)
= -1.4503 / (1 + 2.1441a)
Therefore, the value of tan205 - tan115/tan245 tan335 in terms of a is -1.4503 / (1 + 2.1441a).
Community Answer
If tan 25 degree= a, then what is tge value of tan205-tan115/tan245 ta...
Tan205=tan(180+25)= tan25
tan115=tan(90+25)=- cot25= -1/tan25
tan245=tan(270-25)=cot25
tan335=tan(360-25)=-tan25
=> answer=(1-a^2)/a
tan115=tan(90+25)=- cot25= -1/tan25
tan245=tan(270-25)=cot25
tan335=tan(360-25)=-tan25
=> answer=(1-a^2)/a
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If tan 25 degree= a, then what is tge value of tan205-tan115/tan245 tan335 in terms of a?
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