Question

7.
(i) If sin x = cos x and x is acute, state the
value of x.
(ii) If sec A = cosec A and 0° S AS 90°,
state the value of A.
(iii) If tan 0 = cot 0 and 0° SO S 90°, state
the value of 0.
(iv) If sin x = cos y; write the relation
between x and y, if both the angles x and
y are acute.​

Answer 1

(i)

$sinx = cosx \\ \frac{sinx}{cosx} = 1 \\ tanx = 1 = tan {45}^{o} \\ x = 45$

(ii)

$secx = cosecx \\ \frac{1}{cosx} = \frac{1}{sinx} \\ \\ taking \: reciprocals \: on \: both \: sides \\ \\ cosx = sinx \\ \frac{cosx}{sinx} = 1 \\ cotx = 1 = {45}^{o} \\ x = 45$

(iii)

$tanx = cotx \\ tanx = \frac{1}{tanx} \\ {tan}^{2} x = 1 \\ \\ taking \: square \: roots \: on \: both \: sides \\ \\ tanx = 1 = tan {45}^{o} \\ x = 45$

(iv)

$sinx = cosy \\ sinx = sin( {90}^{o} - y) \\ x = 90 - y \\ x + y = 90$