sin1 degree cos9 tan 5
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Class 11
>>Maths
>>Trigonometric Functions
>>Trigonometric Functions of Sum and Difference of Two angles
>>Prove that cos 9^0 + sin 9^0cos 9^0 -
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Prove that
cos9
0
−sin9
0
cos9
0
+sin9
0
=cot36
0
Medium
Solution
verified
Verified by Toppr
LHS =
(cos9
∘
−sin9
∘
)
(cos9
∘
+sin9
∘
)
Divide by Nr and Dr by cos9
∘
LHS =
1−tan9
∘
1+tan9
∘
=
1−tan45
∘
tan9
∘
tan45
∘
+tan9
∘
where tan45
∘
=1
=tan(45+9) using compound angles formula
=tan54
∘
=tan(90−36)=cot36
∘
Hence Proved
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