in a right angled triangle, if tan A =root2-1 then find the value of tan A /(1+tan²A)
Answers
Answer:
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Step-by-step explanation:
Solution : -
tanA=
2
−1
we know tanA=
B
P
=
1
2
−1
∴H=
(
2
−1)
2
+1
2
=
4−2
2
∴sinA=
4−2
2
2
−1
cosA=
4−2
2
1
∴sinAcosA=
4
−2
2
2
−1
×
4−2
2
1
=
4−2
2
2
−1
=
4−2
2
2
−1
×
4+2
2
4+2
2
=
16−8
4
2
+4−4−2
2
=
8
2
2
=
4
2
Answer:
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Class 11
>>Maths
>>Trigonometric Functions
>>Trigonometric Equations
>>If tan A = √(2) - 1,show that sin A cos
Question
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If tanA=
2
−1,showthatsinAcosA=
4
2
.
Medium
Solution
verified
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Solution : -
tanA=
2
−1
we know tanA=
B
P
=
1
2
−1
∴H=
(
2
−1)
2
+1
2
=
4−2
2
∴sinA=
4−2
2
2
−1
cosA=
4−2
2
1
∴sinAcosA=
4
−2
2
2
−1
×
4−2
2
1
=
4−2
2
2
−1
=
4−2
2
2
−1
×
4+2
2
4+2
2
=
16−8
4
2
+4−4−2
2
=
8
2
2
=
4
2