Answer
Verified
494.7k+ views
Hint: Use the formula of $\tan (A + B) = \dfrac{{\tan A + \tan B}}{{1 - \tan A\tan B}}$ and $\tan (A - B) = \dfrac{{\tan A - \tan B}}{{1 + \tan A\tan B}}$
Therefore, if we put the above formulas to the given equation, it becomes,
$\tan \left( {\dfrac{\pi }{4} + \theta } \right) \times \tan \left( {\dfrac{\pi }{4} - \theta } \right)$
$\dfrac{{\tan \dfrac{\pi }{4} + \tan \theta }}{{1 - \tan \dfrac{\pi }{4}\tan \theta }} \times \dfrac{{\tan \dfrac{\pi }{4} - \tan \theta }}{{1 + \tan \dfrac{\pi }{4}\tan \theta }}$
The next step is to equate$\tan \left( {\dfrac{\pi }{4}} \right) = 1$,
$\dfrac{{1 + \tan \theta }}{{1 - \tan \theta }} \times \dfrac{{1 - \tan \theta }}{{1 + \tan \theta }}$
Cancel out the common terms in denominator with numerators, we are left with,
$1 \times 1 = 1$
Hence Proved!
Note: Use the necessary formula to solve the expression. Instead of trying to solve it further, it is simpler to cancel out the terms.
Therefore, if we put the above formulas to the given equation, it becomes,
$\tan \left( {\dfrac{\pi }{4} + \theta } \right) \times \tan \left( {\dfrac{\pi }{4} - \theta } \right)$
$\dfrac{{\tan \dfrac{\pi }{4} + \tan \theta }}{{1 - \tan \dfrac{\pi }{4}\tan \theta }} \times \dfrac{{\tan \dfrac{\pi }{4} - \tan \theta }}{{1 + \tan \dfrac{\pi }{4}\tan \theta }}$
The next step is to equate$\tan \left( {\dfrac{\pi }{4}} \right) = 1$,
$\dfrac{{1 + \tan \theta }}{{1 - \tan \theta }} \times \dfrac{{1 - \tan \theta }}{{1 + \tan \theta }}$
Cancel out the common terms in denominator with numerators, we are left with,
$1 \times 1 = 1$
Hence Proved!
Note: Use the necessary formula to solve the expression. Instead of trying to solve it further, it is simpler to cancel out the terms.
Recently Updated Pages
In order to prevent the spoilage of potato chips they are packed in plastic bags in an atmosphere of
Which body formulates the foreign policy of India class 10 social science ICSE
What is the message of the poem Nine Gold Medals class 10 english ICSE
The aqueous solution of aluminium chloride is acidic due to
When NaCl is dissolved in water the sodium ion becomes
Give the summary of the story the enchanted pool class 10 english ICSE
Trending doubts
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
How do you graph the function fx 4x class 9 maths CBSE
What is pollution? How many types of pollution? Define it
Distinguish between Conventional and nonconventional class 9 social science CBSE
Difference Between Plant Cell and Animal Cell
Find the mode of 10 12 11 10 15 20 19 21 11 9 10 class 10 maths CBSE
How many squares are there in a chess board A 1296 class 11 maths CBSE
Show that the points 11 52 and 9 5 are collinear-class-10-maths-CBSE