Question

Write ‘True’ or ‘False’ and justify your answer. tan 47° / cot 43° = 1


NCERT Class X
Mathematics - Exemplar Problems

Chapter _INTRODUCTION TO TRIGONOMETRY AND ITS APPLICATIONS

Answer 1

tan47/cot43=1
LHS=tan47/cot43=tan47/cot(90-47)                          
=tan47/cot47                                                               (since,cot(90-a)=tana)
=1=RHS
hence prooved

Answer 2

The statement is completely true.

Formula used :

• Tan x = Cot (90-x)

- The above mentioned formula is taken from the formula range of the co-function identities of the trigonometry.

- We use the formula of the co-function trigonometric identities to transform between the following pairs :

Sin to Cos,Tan to Cot,Sec to Cosec and reverse also.

Mathematical proof -

Let,x = 43° (here 43° angle is assumed as variable x in reverse order to apply the formula which is mentioned and elaborated above)

Now,applying the above mentioned formula in the LHS -

Tan 47° / Cot 43° = Tan 47° / Cot (90°-47°) = Tan 47°/Tan47° = 1 = RHS

Hence,the statement is true. (Proved)