Advertisements
Advertisements
Question
Evaluate:
`2(tan35^@/cot55^@)^2 + (cot55^@/tan35^@)^2 - 3(sec40^@/(cosec50^@))`
Advertisements
Solution
`2(tan35^@/cot55^@)^2 + (cot55^@/tan35^@)^2 - 3(sec40^@/(cosec50^@))`
= `2(tan(90^@-55^@)/cot55^@)^2 + (cot(90^@-35^@)/tan35^@)^2 - 3(sec(90^@-50^@)/(cosec50^@))`
= `2(cot55^@/cot55^@)^2 + (tan35^@/tan35^@)^2 - 3((cosec50^@)/(cosec50^@))` ...`[∵ tan (90^@ - theta) = cot theta` `cot(90^@ - theta) = tan theta` ` sec(90^@ - theta) = cosec theta`]
= 2 × (1)2 + (1)2 – 3 × 1
= 2 × 1 + 1 – 3
= 2 + 1 – 3
= 0
APPEARS IN
RELATED QUESTIONS
`\text{Evaluate }\frac{\tan 65^\circ }{\cot 25^\circ}`
Evaluate `(sin 18^@)/(cos 72^@)`
if `cot theta = 1/sqrt3` find the value of `(1 - cos^2 theta)/(2 - sin^2 theta)`
Evaluate.
sin(90° - A) cosA + cos(90° - A) sinA
For triangle ABC, show that : `tan (B + C)/2 = cot A/2`
Use tables to find sine of 10° 20' + 20° 45'
\[\frac{2 \tan 30°}{1 - \tan^2 30°}\] is equal to ______.
If \[\cos \theta = \frac{2}{3}\] then 2 sec2 θ + 2 tan2 θ − 7 is equal to
If tan θ = cot 37°, then the value of θ is
`tan 47^circ/cot 43^circ` = 1
