Question

HEYA....
.
.
.
.
.PLZ SOLVE 7,8 QUESTION

»FOR GENIUS

»15 POINTS

؛

Answer 1

(7)

Answer :

Option (A)

Explanation:

Here I am writing Alpha as A.

= > 2sec^2a - sec^4a - 2cosec^2a + cosec^4a = 15/4

= > 2sec^2a - 2cosec^2a + cosec^4a - sec^4a = 15/4

= > 2(sec^2a - cosec^2a) + (cosec^2a)^2 - (sec^2a)^2 = 15/4

We know that a^2 - b^2 = (a + b)(a - b)

= > 2(sec^2a - 2cosec^2a) + (cosec^2a + sec^2a)(cosec^2a - sec^2a) = 15/4

= > [cosec^2a - sec^2a][cosec^2a + sec^2a - 2] = 15/4

= > [cot^2a + 1 - (1 + tan^2a)][cot^2a + 1 + tan^2a + 1 - 2] = 15/4

= > [cot^2a + tan^2a][cot^2a + tan^2a] = 15/4

= > [cot^4a - tan^4a] = 15/4

= > 4[cot^4a - tan^4a] = 15

= > 4[1/tan^4a - tan^4a] = 15

= > 4[(1 - tan^8a)/tan^4a] = 15

= > 4[1 - tan^8a] = 15tan^4a

= > 4 - 4 tan^8a - 15tan^4a = 0

= > 4tan^8a + 15tan^4a - 4 = 0

= > 4tan^4a * tan^4a + 16tan^4a - tan^4a - 4 = 0

= > tan^4a(4tan^4a - 1) + 4(tan^4a - 1) = 0

= > (4tan^4a - 1)(tan^4a + 4) = 0

= > tan^4a = 1/4 (or) tan^4a = -4

It should be +ve, so tan^4a = 1/4

                                  tan^2a = 1/2

                                  $tana = \frac{1}{ \sqrt{2} }$






(8)

Answer :

Option(A)

Explanation:

Given 3sinx + 4cosx = 5

On Squaring both sides, we get

= > (3sinx + 4cosx)^2 = (5)^2

= > 9sin^2x + 16cos^2x + 24sinxcosx = 25

= > 9(1 - cos^2x) + 16(1 - sin^2x) + 24sinxcosx = 25

= > 9 - 9cos^2x + 16 - 16sin^2x + 24sinxcosx = 25

= > 16 + 9 - 9cos^2x - 16sin^2x + 24sinxcosx = 25

= > 25 - 9cos^2x - 16sin^2x + 24sinxcosx = 25

= > 9cos^2x + 16sin^2x - 24sinxcosx = 0

= > (3cosx - 4sinx)^2 = 0

= > 4sinx - 3cosx = 0


Hope this helps!

Answer 2

Hi,

Please see the attached file!


Thanks