Question

show that :
(1)tan48°tan23°tan42°tan67°=1
(2)cos38°cos52°sin38°sin52°=0​

Answer 1

solution no 1.

L.H.S

$= \tan(48) \tan(42) \tan(23) \tan(67)$

we know that formula

$\tan(90 - 0) = \cot(0)$

$= \tan(90 - 42) \tan(42) \tan(90 - 67) \tan(67)$

$= \cot(42) \tan(42) \cot(67) \tan(67)$

formula

$\tan(0) \times \cot( 0) = 1$

$= 1 \times 1 = 1$

R.H.S. proof that