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Show that : (i) tan\ 48^@ tan 23^@\ t...

Show that :
(i) ` tan\ 48^@ tan 23^@\ tan 42^@tan 67^@=1`
(ii) `cos 38^@\ cos 52^@ - sin 38^@ sin 52^@=0`

Text Solution

Verified by Experts

i) Taking L.H.S, `tan 48^@ tan 23^@ tan 42^@ tan 67^@`
Since `tan (90^@ - θ) = cot θ`
`tan 48^@ tan 23^@ tan 42^@ tan 67^@ = tan (90^@ - 42^@) tan(90^@ - 67^@) tan 42^@ tan 67^@`
`= cot 42° cot 67° tan 42° tan 67°`
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