the value of tan 65 degree - Tan 20 degree - tan 65 degree Tan 20 degree is..... I will mark the one as brainliest who gives answer with complete steps.
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the value of tan 65 degree - Tan 20 degree - tan 65 degree Tan 20 degree is..... I will mark the one as brainliest who gives answer with complete steps.
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To find the value of tan 65 degrees - tan 20 degrees - tan 65 degrees * tan 20 degrees, we can use the trigonometric identity for the difference of tangents.
The trigonometric identity for the difference of tangents is:
tan(A - B) = (tan A - tan B) / (1 + tan A * tan B)
Let's apply this identity to our expression:
tan 65 degrees - tan 20 degrees - tan 65 degrees * tan 20 degrees
= tan(65 - 20) degrees - tan 65 degrees * tan 20 degrees
= tan 45 degrees - tan 65 degrees * tan 20 degrees
Now, we can use the trigonometric identity for tan 45 degrees, which is equal to 1:
tan 45 degrees = 1
Substituting this value into our expression:
1 - tan 65 degrees * tan 20 degrees
Now, we need to find the values of tan 65 degrees and tan 20 degrees. We can use a scientific calculator or trigonometric tables to find these values.
Using a calculator, we find:
tan 65 degrees ≈ 2.1445
tan 20 degrees ≈ 0.3639
Substituting these values into our expression:
1 - 2.1445 * 0.3639
= 1 - 0.7808
= 0.2192
Therefore, the value of tan 65 degrees - tan 20 degrees - tan 65 degrees * tan 20 degrees is approximately 0.2192.